Transform-based image coding method and device for same

ABSTRACT

An image decoding method according to the present document comprises the steps of: receiving residual information in a bitstream, wherein the residual information includes a transform skip flag for each individual component of the current block; deriving corrected transform coefficients, wherein the step for deriving includes a step for setting a variable indicating whether effective coefficients exist at positions other than that of a DC component of the current block to 0 when even one of the values of the transform skip flags for the individual components is 0, and a step for parsing an LFNST index on the basis of the variable being 0; and deriving an LFNST kernel for applying LFNST on the basis of the LFNST index, wherein the variable being 0 may indicate that effective coefficients exist at positions other than that of the DC component.

BACKGROUND OF THE DISCLOSURE Field of the Disclosure

The present disclosure relates to an image coding technique and, moreparticularly, to a method and an apparatus for coding an image based ontransform in an image coding system.

Related Art

Nowadays, the demand for high-resolution and high-quality images/videossuch as 4K, 8K or more ultra high definition (UHD) images/videos hasbeen increasing in various fields. As the image/video data becomeshigher resolution and higher quality, the transmitted information amountor bit amount increases as compared to the conventional image data.Therefore, when image data is transmitted using a medium such as aconventional wired/wireless broadband line or image/video data is storedusing an existing storage medium, the transmission cost and the storagecost thereof are increased.

Further, nowadays, the interest and demand for immersive media such asvirtual reality (VR), artificial reality (AR) content or hologram, orthe like is increasing, and broadcasting for images/videos having imagefeatures different from those of real images, such as a game image isincreasing.

Accordingly, there is a need for a highly efficient image/videocompression technique for effectively compressing and transmitting orstoring, and reproducing information of high resolution and high qualityimages/videos having various features as described above.

SUMMARY OF THE DISCLOSURE Technical Objects

A technical aspect of the present disclosure is to provide a method andan apparatus for increasing image coding efficiency.

Another technical aspect of the present disclosure provides a method andan apparatus is to provide a method and apparatus for increasingefficiency of LFNST index coding.

Yet another technical aspect of the present disclosure is to provide amethod and apparatus for increasing coding efficiency of an LFNST indexbased on a transform skip flag that is signaled for each colorcomponent.

Technical Solutions

According to an embodiment of the present disclosure, provided herein isan image decoding method performed by a decoding apparatus. The methodmay include the steps of receiving residual information from abitstream, wherein the residual information may include a transform skipflag for each individual component of a current block, and derivingmodified transform coefficients, wherein the deriving modified transformcoefficients may include, when any one of the transform skip flag valuesfor the individual components is equal to 0, setting a variableindicating whether or not a significant coefficient is present in anon-DC component position of the current block to 0, parsing an LFNSTindex based on the variable being equal to 0, and deriving an LFNSTkernel for applying the LFNST based on the LFNST index, wherein thevariable being equal to 0 may indicate that the significant coefficientis present in the non-DC component position.

If the current block is a single tree type, a luma transform skip flagfor a luma component, a first chroma transform skip flag for a firstchroma component, and a second chroma transform skip flag for a secondchroma component may be received, and, if any one of a value of the lumatransform skip flag for a luma component, a value of the first chromatransform skip flag for a first chroma component, and a value of thesecond chroma transform skip flag for a second chroma component is equalto 0, the variable may be set to 0.

If the current block is a single tree type, based on ISP being appliedto the current block, the LFNST index may be parsed regardless of thevariable value.

If the current block is a dual tree luma, a luma transform skip flag fora luma component may be received, and, if a value of the luma transformskip flag is equal to 0, the variable may be set to 0.

If the current block is a dual tree luma, based on ISP being applied tothe current block, the LFNST index may be parsed regardless of thevariable value.

If the current block is a dual tree chroma, a first chroma transformskip flag for a first chroma component and a second chroma transformskip flag for a second chroma component may be received, and, if any oneof a value of the first chroma transform skip flag and a value of thesecond chroma transform skip flag is equal to 0, the variable may be setto 0.

The deriving modified transform coefficients may further include, basedon the LFNST index not being equal to 0 and whether or not a value ofthe individual transform skip flag for the color component is equal to0, configuring a plurality of variables for the LFNST.

According to another embodiment of the present disclosure, providedherein is an image encoding method performed by an image encodingapparatus. The method may include the steps of applying LFNST andderiving modified transform coefficients from the transform coefficient,wherein the deriving modified transform coefficients may includechecking a transform skip flag value for each individual component ofthe current block, when any one of the transform skip flag values foreach individual component is equal to 0, setting a variable indicatingwhether or not a significant coefficient is present in a non-DCcomponent position of the current block to 0, and deriving an LFNSTkernel for applying the LFNST based on the variable being equal to 0,wherein the variable being equal to 0 may indicate that the significantcoefficient is present in the non-DC component position.

According to yet another embodiment of the present disclosure, providedherein is a digital storage medium that stores image data includingencoded image information and a bitstream generated according to animage encoding method performed by an encoding apparatus.

According to yet another embodiment of the present disclosure, providedherein is a digital storage medium that stores image data includingencoded image information and a bitstream to cause a decoding apparatusto perform the image decoding method.

Effects of the Disclosure

According to the present disclosure, overall image/video compressionefficiency may be increased.

According to the present disclosure, efficiency in LFNST index codingmay be increased.

According to the present disclosure, coding efficiency of an LFNST indexmay be increased based on a transform skip flag that is signaled foreach color component.

Effects that can be obtained through specific examples of the presentspecification are not limited to the effects listed above. For example,various technical effects that a person having ordinary skill in therelated art can understand or derive from the present specification mayexist. Accordingly, specific effects of the present specification arenot limited to those explicitly described in the present specification,and can include various effects that can be understood or derived fromthe technical characteristics of the present specification.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 schematically illustrates an example of a video/image codingsystem to which the present disclosure is applicable.

FIG. 2 is a diagram schematically illustrating a configuration of avideo/image encoding apparatus to which the present disclosure isapplicable.

FIG. 3 is a diagram schematically illustrating a configuration of avideo/image decoding apparatus to which the present disclosure isapplicable.

FIG. 4 is schematically illustrates a multiple transform schemeaccording to an embodiment of the present document.

FIG. 5 exemplarily shows intra directional modes of 65 predictiondirections.

FIG. 6 is a diagram for explaining RST according to an embodiment of thepresent.

FIG. 7 is a diagram illustrating a sequence of arranging output data ofa forward primary transformation into a one-dimensional vector accordingto an example.

FIG. 8 is a diagram illustrating a sequence of arranging output data ofa forward secondary transform into a two-dimensional block according toan example.

FIG. 9 is a diagram illustrating wide-angle intra prediction modesaccording to an embodiment of the present document.

FIG. 10 is a diagram illustrating a block shape to which LFNST isapplied.

FIG. 11 is a diagram illustrating a disposition of output data of aforward LFNST according to an embodiment.

FIG. 12 is a diagram illustrating that the number of output data for aforward LFNST is limited to a maximum of 16 according to an example.

FIG. 13 is a diagram illustrating zero-out in a block to which 4×4 LFNSTis applied according to an example.

FIG. 14 is a diagram illustrating zero-out in a block to which 8×8 LFNSTis applied according to an example.

FIG. 15 is a diagram for describing a method of decoding an imageaccording to an example.

FIG. 16 is a diagram for describing a method of encoding an imageaccording to an example.

FIG. 17 is a diagram exemplarily illustrating a structural diagram of acontent streaming system to which the present disclosure is applied.

DESCRIPTION OF EXEMPLARY EMBODIMENTS

While the present disclosure may be susceptible to various modificationsand include various embodiments, specific embodiments thereof have beenshown in the drawings by way of example and will now be described indetail. However, this is not intended to limit the present disclosure tothe specific embodiments disclosed herein. The terminology used hereinis for the purpose of describing specific embodiments only, and is notintended to limit technical idea of the present disclosure. The singularforms may include the plural forms unless the context clearly indicatesotherwise. The terms such as “include” and “have” are intended toindicate that features, numbers, steps, operations, elements,components, or combinations thereof used in the following descriptionexist, and thus should not be understood as that the possibility ofexistence or addition of one or more different features, numbers, steps,operations, elements, components, or combinations thereof is excluded inadvance.

Meanwhile, each component on the drawings described herein isillustrated independently for convenience of description as tocharacteristic functions different from each other, and however, it isnot meant that each component is realized by a separate hardware orsoftware. For example, any two or more of these components may becombined to form a single component, and any single component may bedivided into plural components. The embodiments in which components arecombined and/or divided will belong to the scope of the patent right ofthe present disclosure as long as they do not depart from the essence ofthe present disclosure.

Hereinafter, preferred embodiments of the present disclosure will beexplained in more detail while referring to the attached drawings. Inaddition, the same reference signs are used for the same components onthe drawings, and repeated descriptions for the same components will beomitted.

This document relates to video/image coding. For example, themethod/example disclosed in this document may relate to a VVC (VersatileVideo Coding) standard (ITU-T Rec. H.266), a next-generation video/imagecoding standard after VVC, or other video coding related standards(e.g., HEVC (High Efficiency Video Coding) standard (ITU-T Rec. H.265),EVC (essential video coding) standard, AVS2 standard, etc.).

In this document, a variety of embodiments relating to video/imagecoding may be provided, and, unless specified to the contrary, theembodiments may be combined to each other and be performed.

In this document, a video may mean a set of a series of images overtime. Generally a picture means a unit representing an image at aspecific time zone, and a slice/tile is a unit constituting a part ofthe picture. The slice/tile may include one or more coding tree units(CTUs). One picture may be constituted by one or more slices/tiles. Onepicture may be constituted by one or more tile groups. One tile groupmay include one or more tiles.

A pixel or a pel may mean a smallest unit constituting one picture (orimage). Also, ‘sample’ may be used as a term corresponding to a pixel. Asample may generally represent a pixel or a value of a pixel, and mayrepresent only a pixel/pixel value of a luma component or only apixel/pixel value of a chroma component. Alternatively, the sample mayrefer to a pixel value in the spatial domain, or when this pixel valueis converted to the frequency domain, it may refer to a transformcoefficient in the frequency domain.

A unit may represent the basic unit of image processing. The unit mayinclude at least one of a specific region and information related to theregion. One unit may include one luma block and two chroma (e.g., cb,cr) blocks. The unit and a term such as a block, an area, or the likemay be used in place of each other according to circumstances. In ageneral case, an M×N block may include a set (or an array) of samples(or sample arrays) or transform coefficients consisting of M columns andN rows.

In this document, the term “/” and “,” should be interpreted to indicate“and/or.” For instance, the expression “A/B” may mean “A and/or B.”Further, “A, B” may mean “A and/or B.” Further, “A/B/C” may mean “atleast one of A, B, and/or C.” Also, “A/B/C” may mean “at least one of A,B, and/or C.”

Further, in the document, the term “or” should be interpreted toindicate “and/or.” For instance, the expression “A or B” may include 1)only A, 2) only B, and/or 3) both A and B. In other words, the term “or”in this document should be interpreted to indicate “additionally oralternatively.”

In the present disclosure, “at least one of A and B” may mean “only A”,“only B”, or “both A and B”. In addition, in the present disclosure, theexpression “at least one of A or B” or “at least one of A and/or B” maybe interpreted as “at least one of A and B”.

In addition, in the present disclosure, “at least one of A, B, and C”may mean “only A”, “only B”, “only C”, or “any combination of A, B, andC”. In addition, “at least one of A, B, or C” or “at least one of A, B,and/or C” may mean “at least one of A, B, and C”.

In addition, a parenthesis used in the present disclosure may mean “forexample”. Specifically, when indicated as “prediction (intraprediction)”, it may mean that “intra prediction” is proposed as anexample of “prediction”. In other words, the “prediction” of the presentdisclosure is not limited to “intra prediction”, and “intra prediction”may be proposed as an example of “prediction”. In addition, whenindicated as “prediction (i.e., intra prediction)”, it may also meanthat “intra prediction” is proposed as an example of “prediction”.

Technical features individually described in one figure in the presentdisclosure may be individually implemented or may be simultaneouslyimplemented.

FIG. 1 schematically illustrates an example of a video/image codingsystem to which the present disclosure is applicable.

Referring to FIG. 1 , the video/image coding system may include a firstdevice (source device) and a second device (receive device). The sourcedevice may deliver encoded video/image information or data in the formof a file or streaming to the receive device via a digital storagemedium or network.

The source device may include a video source, an encoding apparatus, anda transmitter. The receive device may include a receiver, a decodingapparatus, and a renderer. The encoding apparatus may be called avideo/image encoding apparatus, and the decoding apparatus may be calleda video/image decoding apparatus. The transmitter may be included in theencoding apparatus. The receiver may be included in the decodingapparatus. The renderer may include a display, and the display may beconfigured as a separate device or an external component.

The video source may obtain a video/image through a process ofcapturing, synthesizing, or generating a video/image. The video sourcemay include a video/image capture device and/or a video/image generatingdevice. The video/image capture device may include, for example, one ormore cameras, video/image archives including previously capturedvideo/images, or the like. The video/image generating device mayinclude, for example, a computer, a tablet and a smartphone, and may(electronically) generate a video/image. For example, a virtualvideo/image may be generated through a computer or the like. In thiscase, the video/image capturing process may be replaced by a process ofgenerating related data.

The encoding apparatus may encode an input video/image. The encodingapparatus may perform a series of procedures such as prediction,transform, and quantization for compression and coding efficiency. Theencoded data (encoded video/image information) may be output in the formof a bitstream.

The transmitter may transmit the encoded video/image information or dataoutput in the form of a bitstream to the receiver of the receive devicethrough a digital storage medium or a network in the form of a file orstreaming. The digital storage medium may include various storagemediums such as USB, SD, CD, DVD, Blu-ray, HDD, SSD, and the like. Thetransmitter may include an element for generating a media file through apredetermined file format, and may include an element for transmissionthrough a broadcast/communication network. The receiver mayreceive/extract the bitstream and transmit the received/extractedbitstream to the decoding apparatus.

The decoding apparatus may decode a video/image by performing a seriesof procedures such as dequantization, inverse transform, prediction, andthe like corresponding to the operation of the encoding apparatus.

The renderer may render the decoded video/image. The renderedvideo/image may be displayed through the display.

FIG. 2 is a diagram schematically illustrating a configuration of avideo/image encoding apparatus to which the present disclosure isapplicable. Hereinafter, what is referred to as the video encodingapparatus may include an image encoding apparatus.

Referring to FIG. 2 , the encoding apparatus 200 may include an imagepartitioner 210, a predictor 220, a residual processor 230, an entropyencoder 240, an adder 250, a filter 260, and a memory 270. The predictor220 may include an inter predictor 221 and an intra predictor 222. Theresidual processor 230 may include a transformer 232, a quantizer 233, adequantizer 234, an inverse transformer 235. The residual processor 230may further include a subtractor 231. The adder 250 may be called areconstructor or reconstructed block generator. The image partitioner210, the predictor 220, the residual processor 230, the entropy encoder240, the adder 250, and the filter 260, which have been described above,may be constituted by one or more hardware components (e.g., encoderchipsets or processors) according to an embodiment. Further, the memory270 may include a decoded picture buffer (DPB), and may be constitutedby a digital storage medium. The hardware component may further includethe memory 270 as an internal/external component.

The image partitioner 210 may partition an input image (or a picture ora frame) input to the encoding apparatus 200 into one or more processingunits. As one example, the processing unit may be called a coding unit(CU). In this case, starting with a coding tree unit (CTU) or thelargest coding unit (LCU), the coding unit may be recursivelypartitioned according to the Quad-tree binary-tree ternary-tree (QTBTTT)structure. For example, one coding unit may be divided into a pluralityof coding units of a deeper depth based on the quad-tree structure, thebinary-tree structure, and/or the ternary structure. In this case, forexample, the quad-tree structure may be applied first and thebinary-tree structure and/or the ternary structure may be applied later.Alternatively, the binary-tree structure may be applied first. Thecoding procedure according to the present disclosure may be performedbased on the final coding unit which is not further partitioned. In thiscase, the maximum coding unit may be used directly as a final codingunit based on coding efficiency according to the image characteristic.Alternatively, the coding unit may be recursively partitioned intocoding units of a further deeper depth as needed, so that the codingunit of an optimal size may be used as a final coding unit. Here, thecoding procedure may include procedures such as prediction, transform,and reconstruction, which will be described later. As another example,the processing unit may further include a prediction unit (PU) or atransform unit (TU). In this case, the prediction unit and the transformunit may be split or partitioned from the above-described final codingunit. The prediction unit may be a unit of sample prediction, and thetransform unit may be a unit for deriving a transform coefficient and/ora unit for deriving a residual signal from a transform coefficient.

The unit and a term such as a block, an area, or the like may be used inplace of each other according to circumstances. In a general case, anM×N block may represent a set of samples or transform coefficientsconsisting of M columns and N rows. The sample may generally represent apixel or a value of a pixel, and may represent only a pixel/pixel valueof a luma component, or only a pixel/pixel value of a chroma component.The sample may be used as a term corresponding to a pixel or a pel ofone picture (or image).

The subtractor 231 subtracts a prediction signal (predicted block,prediction sample array) output from the predictor 220 from an inputimage signal (original block, original sample array) to generate aresidual signal (residual block, residual sample array), and thegenerated residual signal is transmitted to the transformer 232. Thepredictor 220 may perform prediction on a processing target block(hereinafter, referred to as ‘current block’), and may generate apredicted block including prediction samples for the current block. Thepredictor 220 may determine whether intra prediction or inter predictionis applied on a current block or CU basis. As discussed later in thedescription of each prediction mode, the predictor may generate variousinformation relating to prediction, such as prediction mode information,and transmit the generated information to the entropy encoder 240. Theinformation on the prediction may be encoded in the entropy encoder 240and output in the form of a bitstream.

The intra predictor 222 may predict the current block by referring tosamples in the current picture. The referred samples may be located inthe neighbor of or apart from the current block according to theprediction mode. In the intra prediction, prediction modes may include aplurality of non-directional modes and a plurality of directional modes.The non-directional modes may include, for example, a DC mode and aplanar mode. The directional mode may include, for example, 33directional prediction modes or 65 directional prediction modesaccording to the degree of detail of the prediction direction. However,this is merely an example, and more or less directional prediction modesmay be used depending on a setting. The intra predictor 222 maydetermine the prediction mode applied to the current block by using theprediction mode applied to the neighboring block.

The inter predictor 221 may derive a predicted block for the currentblock based on a reference block (reference sample array) specified by amotion vector on a reference picture. At this time, in order to reducethe amount of motion information transmitted in the inter predictionmode, the motion information may be predicted on a block, subblock, orsample basis based on correlation of motion information between theneighboring block and the current block. The motion information mayinclude a motion vector and a reference picture index. The motioninformation may further include inter prediction direction (L0prediction, L1 prediction, Bi prediction, etc.) information. In the caseof inter prediction, the neighboring block may include a spatialneighboring block existing in the current picture and a temporalneighboring block existing in the reference picture. The referencepicture including the reference block and the reference pictureincluding the temporal neighboring block may be same to each other ordifferent from each other. The temporal neighboring block may be calleda collocated reference block, a collocated CU (colCU), and the like, andthe reference picture including the temporal neighboring block may becalled a collocated picture (colPic). For example, the inter predictor221 may configure a motion information candidate list based onneighboring blocks and generate information indicating which candidateis used to derive a motion vector and/or a reference picture index ofthe current block. Inter prediction may be performed based on variousprediction modes. For example, in the case of a skip mode and a mergemode, the inter predictor 221 may use motion information of theneighboring block as motion information of the current block. In theskip mode, unlike the merge mode, the residual signal may not betransmitted. In the case of the motion information prediction (motionvector prediction, MVP) mode, the motion vector of the neighboring blockmay be used as a motion vector predictor and the motion vector of thecurrent block may be indicated by signaling a motion vector difference.

The predictor 220 may generate a prediction signal based on variousprediction methods. For example, the predictor may apply intraprediction or inter prediction for prediction on one block, and, aswell, may apply intra prediction and inter prediction at the same time.This may be called combined inter and intra prediction (CIIP). Further,the predictor may be based on an intra block copy (IBC) prediction mode,or a palette mode in order to perform prediction on a block. The IBCprediction mode or palette mode may be used for content image/videocoding of a game or the like, such as screen content coding (SCC).Although the IBC basically performs prediction in a current block, itcan be performed similarly to inter prediction in that it derives areference block in a current block. That is, the IBC may use at leastone of inter prediction techniques described in the present disclosure.

The prediction signal generated through the inter predictor 221 and/orthe intra predictor 222 may be used to generate a reconstructed signalor to generate a residual signal. The transformer 232 may generatetransform coefficients by applying a transform technique to the residualsignal. For example, the transform technique may include at least one ofa discrete cosine transform (DCT), a discrete sine transform (DST), aKarhunen-Loève transform (KLT), a graph-based transform (GBT), or aconditionally non-linear transform (CNT). Here, the GBT means transformobtained from a graph when relationship information between pixels isrepresented by the graph. The CNT refers to transform obtained based ona prediction signal generated using all previously reconstructed pixels.In addition, the transform process may be applied to square pixel blockshaving the same size or may be applied to blocks having a variable sizerather than the square one.

The quantizer 233 may quantize the transform coefficients and transmitthem to the entropy encoder 240, and the entropy encoder 240 may encodethe quantized signal (information on the quantized transformcoefficients) and output the encoded signal in a bitstream. Theinformation on the quantized transform coefficients may be referred toas residual information. The quantizer 233 may rearrange block typequantized transform coefficients into a one-dimensional vector formbased on a coefficient scan order, and generate information on thequantized transform coefficients based on the quantized transformcoefficients of the one-dimensional vector form. The entropy encoder 240may perform various encoding methods such as, for example, exponentialGolomb, context-adaptive variable length coding (CAVLC),context-adaptive binary arithmetic coding (CABAC), and the like. Theentropy encoder 240 may encode information necessary for video/imagereconstruction other than quantized transform coefficients (e.g. valuesof syntax elements, etc.) together or separately. Encoded information(e.g., encoded video/image information) may be transmitted or stored ona unit basis of a network abstraction layer (NAL) in the form of abitstream. The video/image information may further include informationon various parameter sets such as an adaptation parameter set (APS), apicture parameter set (PPS), a sequence parameter set (SPS), a videoparameter set (VPS) or the like. Further, the video/image informationmay further include general constraint information. In the presentdisclosure, information and/or syntax elements which aretransmitted/signaled to the decoding apparatus from the encodingapparatus may be included in video/image information. The video/imageinformation may be encoded through the above-described encodingprocedure and included in the bitstream. The bitstream may betransmitted through a network, or stored in a digital storage medium.Here, the network may include a broadcast network, a communicationnetwork and/or the like, and the digital storage medium may includevarious storage media such as USB, SD, CD, DVD, Blu-ray, HDD, SSD, andthe like. A transmitter (not shown) which transmits a signal output fromthe entropy encoder 240 and/or a storage (not shown) which stores it maybe configured as an internal/external element of the encoding apparatus200, or the transmitter may be included in the entropy encoder 240.

Quantized transform coefficients output from the quantizer 233 may beused to generate a prediction signal. For example, by applyingdequantization and inverse transform to quantized transform coefficientsthrough the dequantizer 234 and the inverse transformer 235, theresidual signal (residual block or residual samples) may bereconstructed. The adder 155 adds the reconstructed residual signal to aprediction signal output from the inter predictor 221 or the intrapredictor 222, so that a reconstructed signal (reconstructed picture,reconstructed block, reconstructed sample array) may be generated. Whenthere is no residual for a processing target block as in a case wherethe skip mode is applied, the predicted block may be used as areconstructed block. The adder 250 may be called a reconstructor or areconstructed block generator. The generated reconstructed signal may beused for intra prediction of a next processing target block in thecurrent block, and as described later, may be used for inter predictionof a next picture through filtering.

Meanwhile, in the picture encoding and/or reconstructing process, lumamapping with chroma scaling (LMCS) may be applied.

The filter 260 may improve subjective/objective video quality byapplying the filtering to the reconstructed signal. For example, thefilter 260 may generate a modified reconstructed picture by applyingvarious filtering methods to the reconstructed picture, and may storethe modified reconstructed picture in the memory 270, specifically inthe DPB of the memory 270. The various filtering methods may include,for example, deblocking filtering, sample adaptive offset, an adaptiveloop filter, a bilateral filter or the like. As discussed later in thedescription of each filtering method, the filter 260 may generatevarious information relating to filtering, and transmit the generatedinformation to the entropy encoder 240. The information on the filteringmay be encoded in the entropy encoder 240 and output in the form of abitstream.

The modified reconstructed picture which has been transmitted to thememory 270 may be used as a reference picture in the inter predictor221. Through this, the encoding apparatus can avoid prediction mismatchin the encoding apparatus 100 and a decoding apparatus when the interprediction is applied, and can also improve coding efficiency.

The memory 270 DPB may store the modified reconstructed picture in orderto use it as a reference picture in the inter predictor 221. The memory270 may store motion information of a block in the current picture, fromwhich motion information has been derived (or encoded) and/or motioninformation of blocks in an already reconstructed picture. The storedmotion information may be transmitted to the inter predictor 221 to beutilized as motion information of a neighboring block or motioninformation of a temporal neighboring block. The memory 270 may storereconstructed samples of reconstructed blocks in the current picture,and transmit them to the intra predictor 222.

FIG. 3 is a diagram schematically illustrating a configuration of avideo/image decoding apparatus to which the present disclosure isapplicable.

Referring to FIG. 3 , the video decoding apparatus 300 may include anentropy decoder 310, a residual processor 320, a predictor 330, an adder340, a filter 350 and a memory 360. The predictor 330 may include aninter predictor 331 and an intra predictor 332. The residual processor320 may include a dequantizer 321 and an inverse transformer 321. Theentropy decoder 310, the residual processor 320, the predictor 330, theadder 340, and the filter 350, which have been described above, may beconstituted by one or more hardware components (e.g., decoder chipsetsor processors) according to an embodiment. Further, the memory 360 mayinclude a decoded picture buffer (DPB), and may be constituted by adigital storage medium. The hardware component may further include thememory 360 as an internal/external component.

When a bitstream including video/image information is input, thedecoding apparatus 300 may reconstruct an image correspondingly to aprocess by which video/image information has been processed in theencoding apparatus of FIG. 2 . For example, the decoding apparatus 300may derive units/blocks based on information relating to block partitionobtained from the bitstream. The decoding apparatus 300 may performdecoding by using a processing unit applied in the encoding apparatus.Therefore, the processing unit of decoding may be, for example, a codingunit, which may be partitioned along the quad-tree structure, thebinary-tree structure, and/or the ternary-tree structure from a codingtree unit or a largest coding unit. One or more transform units may bederived from the coding unit. And, the reconstructed image signaldecoded and output through the decoding apparatus 300 may be reproducedthrough a reproducer.

The decoding apparatus 300 may receive a signal output from the encodingapparatus of FIG. 2 in the form of a bitstream, and the received signalmay be decoded through the entropy decoder 310. For example, the entropydecoder 310 may parse the bitstream to derive information (e.g.,video/image information) required for image reconstruction (or picturereconstruction). The video/image information may further includeinformation on various parameter sets such as an adaptation parameterset (APS), a picture parameter set (PPS), a sequence parameter set(SPS), a video parameter set (VPS) or the like. Further, the video/imageinformation may further include general constraint information. Thedecoding apparatus may decode a picture further based on information onthe parameter set and/or the general constraint information. In thepresent disclosure, signaled/received information and/or syntaxelements, which will be described later, may be decoded through thedecoding procedure and be obtained from the bitstream. For example, theentropy decoder 310 may decode information in the bitstream based on acoding method such as exponential Golomb encoding, CAVLC, CABAC, or thelike, and may output a value of a syntax element necessary for imagereconstruction and quantized values of a transform coefficient regardinga residual. More specifically, a CABAC entropy decoding method mayreceive a bin corresponding to each syntax element in a bitstream,determine a context model using decoding target syntax elementinformation and decoding information of neighboring and decoding targetblocks, or information of symbol/bin decoded in a previous step, predictbin generation probability according to the determined context model andperform arithmetic decoding of the bin to generate a symbolcorresponding to each syntax element value. Here, the CABAC entropydecoding method may update the context model using information of asymbol/bin decoded for a context model of the next symbol/bin afterdetermination of the context model. Information on prediction amonginformation decoded in the entropy decoder 310 may be provided to thepredictor (inter predictor 332 and intra predictor 331), and residualvalues, that is, quantized transform coefficients, on which entropydecoding has been performed in the entropy decoder 310, and associatedparameter information may be input to the residual processor 320. Theresidual processor 320 may derive a residual signal (residual block,residual samples, residual sample array). Further, information onfiltering among information decoded in the entropy decoder 310 may beprovided to the filter 350. Meanwhile, a receiver (not shown) whichreceives a signal output from the encoding apparatus may furtherconstitute the decoding apparatus 300 as an internal/external element,and the receiver may be a component of the entropy decoder 310.Meanwhile, the decoding apparatus according to the present disclosuremay be called a video/image/picture coding apparatus, and the decodingapparatus may be classified into an information decoder(video/image/picture information decoder) and a sample decoder(video/image/picture sample decoder). The information decoder mayinclude the entropy decoder 310, and the sample decoder may include atleast one of the dequantizer 321, the inverse transformer 322, the adder340, the filter 350, the memory 360, the inter predictor 332, and theintra predictor 331.

The dequantizer 321 may output transform coefficients by dequantizingthe quantized transform coefficients. The dequantizer 321 may rearrangethe quantized transform coefficients in the form of a two-dimensionalblock. In this case, the rearrangement may perform rearrangement basedon an order of coefficient scanning which has been performed in theencoding apparatus. The dequantizer 321 may perform dequantization onthe quantized transform coefficients using quantization parameter (e.g.,quantization step size information), and obtain transform coefficients.

The deqauntizer 322 obtains a residual signal (residual block, residualsample array) by inverse transforming transform coefficients.

The predictor may perform prediction on the current block, and generatea predicted block including prediction samples for the current block.The predictor may determine whether intra prediction or inter predictionis applied to the current block based on the information on predictionoutput from the entropy decoder 310, and specifically may determine anintra/inter prediction mode.

The predictor may generate a prediction signal based on variousprediction methods. For example, the predictor may apply intraprediction or inter prediction for prediction on one block, and, aswell, may apply intra prediction and inter prediction at the same time.This may be called combined inter and intra prediction (CIIP). Inaddition, the predictor may perform intra block copy (IBC) forprediction on a block. The intra block copy may be used for contentimage/video coding of a game or the like, such as screen content coding(SCC). Although the IBC basically performs prediction in a currentblock, it can be performed similarly to inter prediction in that itderives a reference block in a current block. That is, the IBC may useat least one of inter prediction techniques described in the presentdisclosure.

The intra predictor 331 may predict the current block by referring tothe samples in the current picture. The referred samples may be locatedin the neighbor of or apart from the current block according to theprediction mode. In the intra prediction, prediction modes may include aplurality of non-directional modes and a plurality of directional modes.The intra predictor 331 may determine the prediction mode applied to thecurrent block by using the prediction mode applied to the neighboringblock.

The inter predictor 332 may derive a predicted block for the currentblock based on a reference block (reference sample array) specified by amotion vector on a reference picture. At this time, in order to reducethe amount of motion information transmitted in the inter predictionmode, the motion information may be predicted on a block, subblock, orsample basis based on correlation of motion information between theneighboring block and the current block. The motion information mayinclude a motion vector and a reference picture index. The motioninformation may further include inter prediction direction (L0prediction, L1 prediction, Bi prediction, etc.) information. In the caseof inter prediction, the neighboring block may include a spatialneighboring block existing in the current picture and a temporalneighboring block existing in the reference picture. For example, theinter predictor 332 may configure a motion information candidate listbased on neighboring blocks, and derive a motion vector and/or areference picture index of the current block based on received candidateselection information. Inter prediction may be performed based onvarious prediction modes, and the information on prediction may includeinformation indicating a mode of inter prediction for the current block.

The adder 340 may generate a reconstructed signal (reconstructedpicture, reconstructed block, reconstructed sample array) by adding theobtained residual signal to the prediction signal (predicted block,prediction sample array) output from the predictor 330. When there is noresidual for a processing target block as in a case where the skip modeis applied, the predicted block may be used as a reconstructed block.

The adder 340 may be called a reconstructor or a reconstructed blockgenerator. The generated reconstructed signal may be used for intraprediction of a next processing target block in the current block, andas described later, may be output through filtering or be used for interprediction of a next picture.

Meanwhile, in the picture decoding process, luma mapping with chromascaling (LMCS) may be applied.

The filter 350 may improve subjective/objective video quality byapplying the filtering to the reconstructed signal. For example, thefilter 350 may generate a modified reconstructed picture by applyingvarious filtering methods to the reconstructed picture, and may transmitthe modified reconstructed picture in the memory 360, specifically inthe DPB of the memory 360. The various filtering methods may include,for example, deblocking filtering, sample adaptive offset, an adaptiveloop filter, a bilateral filter or the like.

The (modified) reconstructed picture which has been stored in the DPB ofthe memory 360 may be used as a reference picture in the inter predictor332. The memory 360 may store motion information of a block in thecurrent picture, from which motion information has been derived (ordecoded) and/or motion information of blocks in an already reconstructedpicture. The stored motion information may be transmitted to the interpredictor 260 to be utilized as motion information of a neighboringblock or motion information of a temporal neighboring block. The memory360 may store reconstructed samples of reconstructed blocks in thecurrent picture, and transmit them to the intra predictor 331.

In this specification, the examples described in the predictor 330, thedequantizer 321, the inverse transformer 322, and the filter 350 of thedecoding apparatus 300 may be similarly or correspondingly applied tothe predictor 220, the dequantizer 234, the inverse transformer 235, andthe filter 260 of the encoding apparatus 200, respectively.

As described above, prediction is performed in order to increasecompression efficiency in performing video coding. Through this, apredicted block including prediction samples for a current block, whichis a coding target block, may be generated. Here, the predicted blockincludes prediction samples in a space domain (or pixel domain). Thepredicted block may be identically derived in the encoding apparatus andthe decoding apparatus, and the encoding apparatus may increase imagecoding efficiency by signaling to the decoding apparatus not originalsample value of an original block itself but information on residual(residual information) between the original block and the predictedblock. The decoding apparatus may derive a residual block includingresidual samples based on the residual information, generate areconstructed block including reconstructed samples by adding theresidual block to the predicted block, and generate a reconstructedpicture including reconstructed blocks.

The residual information may be generated through transform andquantization procedures. For example, the encoding apparatus may derivea residual block between the original block and the predicted block,derive transform coefficients by performing a transform procedure onresidual samples (residual sample array) included in the residual block,and derive quantized transform coefficients by performing a quantizationprocedure on the transform coefficients, so that it may signalassociated residual information to the decoding apparatus (through abitstream). Here, the residual information may include valueinformation, position information, a transform technique, transformkernel, a quantization parameter or the like of the quantized transformcoefficients. The decoding apparatus may perform aquantization/dequantization procedure and derive the residual samples(or residual sample block), based on residual information. The decodingapparatus may generate a reconstructed block based on a predicted blockand the residual block. The encoding apparatus may derive a residualblock by dequantizing/inverse transforming quantized transformcoefficients for reference for inter prediction of a next picture, andmay generate a reconstructed picture based on this.

FIG. 4 schematically illustrates a multiple transform techniqueaccording to an embodiment of the present disclosure.

Referring to FIG. 4 , a transformer may correspond to the transformer inthe encoding apparatus of foregoing FIG. 2 , and an inverse transformermay correspond to the inverse transformer in the encoding apparatus offoregoing FIG. 2 , or to the inverse transformer in the decodingapparatus of FIG. 3 .

The transformer may derive (primary) transform coefficients byperforming a primary transform based on residual samples (residualsample array) in a residual block (S410). This primary transform may bereferred to as a core transform. Herein, the primary transform may bebased on multiple transform selection (MTS), and when a multipletransform is applied as the primary transform, it may be referred to asa multiple core transform.

The multiple core transform may represent a method of transformingadditionally using discrete cosine transform (DCT) type 2 and discretesine transform (DST) type 7, DCT type 8, and/or DST type 1. That is, themultiple core transform may represent a transform method of transforminga residual signal (or residual block) of a space domain into transformcoefficients (or primary transform coefficients) of a frequency domainbased on a plurality of transform kernels selected from among the DCTtype 2, the DST type 7, the DCT type 8 and the DST type 1. Herein, theprimary transform coefficients may be called temporary transformcoefficients from the viewpoint of the transformer.

In other words, when the conventional transform method is applied,transform coefficients might be generated by applying transform from aspace domain to a frequency domain for a residual signal (or residualblock) based on the DCT type 2. Unlike to this, when the multiple coretransform is applied, transform coefficients (or primary transformcoefficients) may be generated by applying transform from a space domainto a frequency domain for a residual signal (or residual block) based onthe DCT type 2, the DST type 7, the DCT type 8, and/or DST type 1.Herein, the DCT type 2, the DST type 7, the DCT type 8, and the DST type1 may be called a transform type, transform kernel or transform core.These DCT/DST transform types can be defined based on basis functions.

When the multiple core transform is performed, a vertical transformkernel and a horizontal transform kernel for a target block may beselected from among the transform kernels, a vertical transform may beperformed on the target block based on the vertical transform kernel,and a horizontal transform may be performed on the target block based onthe horizontal transform kernel. Here, the horizontal transform mayindicate a transform on horizontal components of the target block, andthe vertical transform may indicate a transform on vertical componentsof the target block. The vertical transform kernel/horizontal transformkernel may be adaptively determined based on a prediction mode and/or atransform index for the target block (CU or subblock) including aresidual block.

Further, according to an example, if the primary transform is performedby applying the MTS, a mapping relationship for transform kernels may beset by setting specific basis functions to predetermined values andcombining basis functions to be applied in the vertical transform or thehorizontal transform. For example, when the horizontal transform kernelis expressed as trTypeHor and the vertical direction transform kernel isexpressed as trTypeVer, a trTypeHor or trTypeVer value of 0 may be setto DCT2, a trTypeHor or trTypeVer value of 1 may be set to DST7, and atrTypeHor or trTypeVer value of 2 may be set to DCT8.

In this case, MTS index information may be encoded and signaled to thedecoding apparatus to indicate any one of a plurality of transformkernel sets. For example, an MTS index of 0 may indicate that bothtrTypeHor and trTypeVer values are 0, an MTS index of 1 may indicatethat both trTypeHor and trTypeVer values are 1, an MTS index of 2 mayindicate that the trTypeHor value is 2 and the trTypeVer value. Is 1, anMTS index of 3 may indicate that the trTypeHor value is 1 and thetrTypeVer value is 2, and an MTS index of 4 may indicate that bothtrTypeHor and trTypeVer values are 2.

In one example, transform kernel sets according to MTS index informationare illustrated in the following table.

TABLE 1 tu_mts_idx[ x0 ][ y0 ] 0 1 2 3 4 trTypeHor 0 1 2 1 2 trTypeVer 01 1 2 2

The transformer may perform a secondary transform based on the (primary)transform coefficients to derive modified (secondary) transformcoefficients (S420). The primary transform is a transform from a spatialdomain to a frequency domain, and the secondary transform refers totransforming into a more compact expression using a correlation existingbetween (primary) transform coefficients. The secondary transform mayinclude a non-separable transform. In this case, the secondary transformmay be referred to as a non-separable secondary transform (NSST) or amode-dependent non-separable secondary transform (MDNSST). The NSST mayrepresent a transform that secondarily transforms (primary) transformcoefficients derived through the primary transform based on anon-separable transform matrix to generate modified transformcoefficients (or secondary transform coefficients) for a residualsignal. Here, the transform may be applied at once without separating(or independently applying a horizontal/vertical transform) a verticaltransform and a horizontal transform to the (primary) transformcoefficients based on the non-separable transform matrix. In otherwords, the NSST is not separately applied to the (primary) transformcoefficients in a vertical direction and a horizontal direction, and mayrepresent, for example, a transform method of rearrangingtwo-dimensional signals (transform coefficients) into a one-dimensionalsignal through a specific predetermined direction (e.g., row-firstdirection or column-first direction) and then generating modifiedtransform coefficients (or secondary transform coefficients) based onthe non-separable transform matrix. For example, a row-first order is todispose in a line in order of a 1st row, a 2nd row, . . . , an Nth rowfor M×N blocks, and a column-first order is to dispose in a line inorder of a 1st column, a 2nd column, . . . , an Mth column for M×Nblocks. The NSST may be applied to a top-left region of a block(hereinafter, referred to as a transform coefficient block) configuredwith (primary) transform coefficients. For example, when both a width Wand height H of the transform coefficient block are 8 or more, an 8×8NSST may be applied to the top-left 8×8 region of the transformcoefficient block. Further, while both the width (W) and height (H) ofthe transform coefficient block are 4 or more, when the width (W) orheight (H) of the transform coefficient block is smaller than 8, 4×4NSST may be applied to the top-left min(8,W)×min(8,H) region of thetransform coefficient block. However, the embodiment is not limitedthereto, and for example, even if only the condition that the width W orthe height H of the transform coefficient block is 4 or greater issatisfied, the 4×4 NSST may be applied to the top-left endmin(8,W)×min(8,H) region of the transform coefficient block.

Specifically, for example, if a 4×4 input block is used, thenon-separable secondary transform may be performed as follows.

The 4×4 input block X may be represented as follows.

$\begin{matrix}{X = \begin{bmatrix}X_{00} & X_{01} & X_{02} & X_{03} \\X_{10} & X_{11} & X_{12} & X_{13} \\X_{20} & X_{21} & X_{22} & X_{23} \\X_{30} & X_{31} & X_{32} & X_{33}\end{bmatrix}} & \left\lbrack {{Equation}1} \right\rbrack\end{matrix}$

If the X is represented in the form of a vector, the vector {right arrowover (X)} may be represented as below.

{right arrow over (X)}=[X ₀₀ X ₀₁ X ₀₂ X ₀₃ X ₁₀ X ₁₁ X ₁₂ X ₁₃ X ₂₀ X₂₁ X ₂₂ X ₂₃ X ₃₀ X ₃₁ X ₃₂ X ₃₃]^(T)  [Equation 2]

In Equation 2, the vector X is a one-dimensional vector obtained byrearranging the two-dimensional block X of Equation 1 according to therow-first order.

In this case, the secondary non-separable transform may be calculated asbelow.

=T·

  [Equation 3]

In this equation, {right arrow over (F)} represents a transformcoefficient vector, and T represents a 16×16 (non-separable) transformmatrix.

Through foregoing Equation 3, a 16×1 transform coefficient vector {rightarrow over (F)} may be derived, and the {right arrow over (F)} may bere-organized into a 4×4 block through a scan order (horizontal,vertical, diagonal and the like). However, the above-describedcalculation is an example, and hypercube-Givens transform (HyGT) or thelike may be used for the calculation of the non-separable secondarytransform in order to reduce the computational complexity of thenon-separable secondary transform.

Meanwhile, in the non-separable secondary transform, a transform kernel(or transform core, transform type) may be selected to be modedependent. In this case, the mode may include the intra prediction modeand/or the inter prediction mode.

As described above, the non-separable secondary transform may beperformed based on an 8×8 transform or a 4×4 transform determined basedon the width (W) and the height (H) of the transform coefficient block.The 8×8 transform refers to a transform that is applicable to an 8×8region included in the transform coefficient block when both W and H areequal to or greater than 8, and the 8×8 region may be a top-left 8×8region in the transform coefficient block. Similarly, the 4×4 transformrefers to a transform that is applicable to a 4×4 region included in thetransform coefficient block when both W and H are equal to or greaterthan 4, and the 4×4 region may be a top-left 4×4 region in the transformcoefficient block. For example, an 8×8 transform kernel matrix may be a64×64/16×64 matrix, and a 4×4 transform kernel matrix may be a16×16/8×16 matrix.

Here, to select a mode-dependent transform kernel, two non-separablesecondary transform kernels per transform set for a non-separablesecondary transform may be configured for both the 8×8 transform and the4×4 transform, and there may be four transform sets. That is, fourtransform sets may be configured for the 8×8 transform, and fourtransform sets may be configured for the 4×4 transform. In this case,each of the four transform sets for the 8×8 transform may include two8×8 transform kernels, and each of the four transform sets for the 4×4transform may include two 4×4 transform kernels.

However, as the size of the transform, that is, the size of a region towhich the transform is applied, may be, for example, a size other than8×8 or 4×4, the number of sets may be n, and the number of transformkernels in each set may be k.

The transform set may be referred to as an NSST set or an LFNST set. Aspecific set among the transform sets may be selected, for example,based on the intra prediction mode of the current block (CU orsubblock). A low-frequency non-separable transform (LFNST) may be anexample of a reduced non-separable transform, which will be describedlater, and represents a non-separable transform for a low frequencycomponent.

For reference, for example, the intra prediction mode may include twonon-directional (or non-angular) intra prediction modes and 65directional (or angular) intra prediction modes. The non-directionalintra prediction modes may include a planar intra prediction mode of No.0 and a DC intra prediction mode of No. 1, and the directional intraprediction modes may include 65 intra prediction modes of Nos. 2 to 66.However, this is an example, and this document may be applied even whenthe number of intra prediction modes is different. Meanwhile, in somecases, intra prediction mode No. 67 may be further used, and the intraprediction mode No. 67 may represent a linear model (LM) mode.

FIG. 5 exemplarily shows intra directional modes of 65 predictiondirections.

Referring to FIG. 5 , on the basis of intra prediction mode 34 having aleft upward diagonal prediction direction, the intra prediction modesmay be divided into intra prediction modes having horizontaldirectionality and intra prediction modes having verticaldirectionality. In FIG. 5 , H and V denote horizontal directionality andvertical directionality, respectively, and numerals −32 to 32 indicatedisplacements in 1/32 units on a sample grid position. These numeralsmay represent an offset for a mode index value. Intra prediction modes 2to 33 have the horizontal directionality, and intra prediction modes 34to 66 have the vertical directionality. Strictly speaking, intraprediction mode 34 may be considered as being neither horizontal norvertical, but may be classified as belonging to the horizontaldirectionality in determining a transform set of a secondary transform.This is because input data is transposed to be used for a verticaldirection mode symmetrical on the basis of intra prediction mode 34, andan input data alignment method for a horizontal mode is used for intraprediction mode 34. Transposing input data means that rows and columnsof two-dimensional M×N block data are switched into N×M data. Intraprediction mode 18 and intra prediction mode 50 may represent ahorizontal intra prediction mode and a vertical intra prediction mode,respectively, and intra prediction mode 2 may be referred to as a rightupward diagonal intra prediction mode because intra prediction mode 2has a left reference pixel and performs prediction in a right upwarddirection. Likewise, intra prediction mode 34 may be referred to as aright downward diagonal intra prediction mode, and intra prediction mode66 may be referred to as a left downward diagonal intra prediction mode.

According to an example, the four transform sets according to the intraprediction mode may be mapped, for example, as shown in the followingtable.

TABLE 2 predModeIntra lfnstTrSetIdx predModeIntra < 0 1 0 <=predModeIntra <= 1 0  2 <= predModeIntra <= 12 1 13 <= predModeIntra <=23 2 24 <= predModeIntra <= 44 3 45 <= predModeIntra <= 55 2 56 <=predModeIntra <= 80 1

As shown in Table 2, any one of the four transform sets, that is,lfnstTrSetIdx, may be mapped to any one of four indexes, that is, 0 to3, according to the intra prediction mode.

When it is determined that a specific set is used for the non-separabletransform, one of k transform kernels in the specific set may beselected through a non-separable secondary transform index. An encodingapparatus may derive a non-separable secondary transform indexindicating a specific transform kernel based on a rate-distortion (RD)check and may signal the non-separable secondary transform index to adecoding apparatus. The decoding apparatus may select one of the ktransform kernels in the specific set based on the non-separablesecondary transform index. For example, lfnst index value 0 may refer toa first non-separable secondary transform kernel, lfnst index value 1may refer to a second non-separable secondary transform kernel, andlfnst index value 2 may refer to a third non-separable secondarytransform kernel. Alternatively, lfnst index value 0 may indicate thatthe first non-separable secondary transform is not applied to the targetblock, and lfnst index values 1 to 3 may indicate the three transformkernels.

The transformer may perform the non-separable secondary transform basedon the selected transform kernels, and may obtain modified (secondary)transform coefficients. As described above, the modified transformcoefficients may be derived as transform coefficients quantized throughthe quantizer, and may be encoded and signaled to the decoding apparatusand transferred to the dequantizer/inverse transformer in the encodingapparatus.

Meanwhile, as described above, if the secondary transform is omitted,(primary) transform coefficients, which are an output of the primary(separable) transform, may be derived as transform coefficientsquantized through the quantizer as described above, and may be encodedand signaled to the decoding apparatus and transferred to thedequantizer/inverse transformer in the encoding apparatus.

The inverse transformer may perform a series of procedures in theinverse order to that in which they have been performed in theabove-described transformer. The inverse transformer may receive(dequantized) transformer coefficients, and derive (primary) transformcoefficients by performing a secondary (inverse) transform (S450), andmay obtain a residual block (residual samples) by performing a primary(inverse) transform on the (primary) transform coefficients (S460). Inthis connection, the primary transform coefficients may be calledmodified transform coefficients from the viewpoint of the inversetransformer. As described above, the encoding apparatus and the decodingapparatus may generate the reconstructed block based on the residualblock and the predicted block, and may generate the reconstructedpicture based on the reconstructed block.

The decoding apparatus may further include a secondary inverse transformapplication determinator (or an element to determine whether to apply asecondary inverse transform) and a secondary inverse transformdeterminator (or an element to determine a secondary inverse transform).The secondary inverse transform application determinator may determinewhether to apply a secondary inverse transform. For example, thesecondary inverse transform may be an NSST, an RST, or an LFNST and thesecondary inverse transform application determinator may determinewhether to apply the secondary inverse transform based on a secondarytransform flag obtained by parsing the bitstream. In another example,the secondary inverse transform application determinator may determinewhether to apply the secondary inverse transform based on a transformcoefficient of a residual block.

The secondary inverse transform determinator may determine a secondaryinverse transform. In this case, the secondary inverse transformdeterminator may determine the secondary inverse transform applied tothe current block based on an LFNST (NSST or RST) transform setspecified according to an intra prediction mode. In an embodiment, asecondary transform determination method may be determined depending ona primary transform determination method. Various combinations ofprimary transforms and secondary transforms may be determined accordingto the intra prediction mode. Further, in an example, the secondaryinverse transform determinator may determine a region to which asecondary inverse transform is applied based on the size of the currentblock.

Meanwhile, as described above, if the secondary (inverse) transform isomitted, (dequantized) transform coefficients may be received, theprimary (separable) inverse transform may be performed, and the residualblock (residual samples) may be obtained. As described above, theencoding apparatus and the decoding apparatus may generate thereconstructed block based on the residual block and the predicted block,and may generate the reconstructed picture based on the reconstructedblock.

Meanwhile, in the present disclosure, a reduced secondary transform(RST) in which the size of a transform matrix (kernel) is reduced may beapplied in the concept of NSST in order to reduce the amount ofcomputation and memory required for the non-separable secondarytransform.

Meanwhile, the transform kernel, the transform matrix, and thecoefficient constituting the transform kernel matrix, that is, thekernel coefficient or the matrix coefficient, described in the presentdisclosure may be expressed in 8 bits. This may be a condition forimplementation in the decoding apparatus and the encoding apparatus, andmay reduce the amount of memory required to store the transform kernelwith a performance degradation that can be reasonably accommodatedcompared to the existing 9 bits or 10 bits. In addition, the expressingof the kernel matrix in 8 bits may allow a small multiplier to be used,and may be more suitable for single instruction multiple data (SIMD)instructions used for optimal software implementation.

In the present specification, the term “RST” may mean a transform whichis performed on residual samples for a target block based on a transformmatrix whose size is reduced according to a reduced factor. In the caseof performing the reduced transform, the amount of computation requiredfor transform may be reduced due to a reduction in the size of thetransform matrix. That is, the RST may be used to address thecomputational complexity issue occurring at the non-separable transformor the transform of a block of a great size.

RST may be referred to as various terms, such as reduced transform,reduced secondary transform, reduction transform, simplified transform,simple transform, and the like, and the name which RST may be referredto as is not limited to the listed examples. Alternatively, once the RSTis mainly performed in a low frequency region including a non-zerocoefficient in a transform block, it may be referred to as aLow-Frequency Non-Separable Transform (LFNST). The transform index maybe referred to as an LFNST index.

Meanwhile, when the secondary inverse transform is performed based onRST, the inverse transformer 235 of the encoding apparatus 200 and theinverse transformer 322 of the decoding apparatus 300 may include aninverse reduced secondary transformer which derives modified transformcoefficients based on the inverse RST of the transform coefficients, andan inverse primary transformer which derives residual samples for thetarget block based on the inverse primary transform of the modifiedtransform coefficients. The inverse primary transform refers to theinverse transform of the primary transform applied to the residual. Inthe present disclosure, deriving a transform coefficient based on atransform may refer to deriving a transform coefficient by applying thetransform.

FIG. 6 is a diagram illustrating an RST according to an embodiment ofthe present disclosure.

In the present disclosure, a “target block” may refer to a current blockto be coded, a residual block, or a transform block.

In the RST according to an example, an N-dimensional vector may bemapped to an R-dimensional vector located in another space, so that thereduced transform matrix may be determined, where R is less than N. Nmay mean the square of the length of a side of a block to which thetransform is applied, or the total number of transform coefficientscorresponding to a block to which the transform is applied, and thereduced factor may mean an R/N value. The reduced factor may be referredto as a reduced factor, reduction factor, simplified factor, simplefactor or other various terms. Meanwhile, R may be referred to as areduced coefficient, but according to circumstances, the reduced factormay mean R. Further, according to circumstances, the reduced factor maymean the N/R value.

In an example, the reduced factor or the reduced coefficient may besignaled through a bitstream, but the example is not limited to this.For example, a predefined value for the reduced factor or the reducedcoefficient may be stored in each of the encoding apparatus 200 and thedecoding apparatus 300, and in this case, the reduced factor or thereduced coefficient may not be signaled separately.

The size of the reduced transform matrix according to an example may beR×N less than N×N, the size of a conventional transform matrix, and maybe defined as in Equation 4 below.

$\begin{matrix}{T_{R \times N} = \begin{bmatrix}t_{11} & t_{12} & t_{13} & \ldots & t_{1N} \\t_{21} & t_{22} & t_{23} & & t_{2N} \\ & \vdots & & \ddots & \vdots \\t_{R1} & t_{R2} & t_{R3} & \ldots & t_{RN}\end{bmatrix}} & \left\lbrack {{Equation}4} \right\rbrack\end{matrix}$

The matrix T in the Reduced Transform block shown in (a) of FIG. 6 maymean the matrix T_(R×N) of Equation 4. As shown in (a) of FIG. 6 , whenthe reduced transform matrix T_(R×N) is multiplied to residual samplesfor the target block, transform coefficients for the target block may bederived.

In an example, if the size of the block to which the transform isapplied is 8×8 and R=16 (i.e., R/N=16/64=¼), then the RST according to(a) of FIG. 6 may be expressed as a matrix operation as shown inEquation 5 below. In this case, memory and multiplication calculationcan be reduced to approximately ¼ by the reduced factor.

In the present disclosure, a matrix operation may be understood as anoperation of multiplying a column vector by a matrix, disposed on theleft of the column vector, to obtain a column vector.

$\begin{matrix}{\begin{bmatrix}t_{1,1} & t_{1,2} & t_{1,3} & \ldots & t_{1,64} \\t_{2,1} & t_{2,2} & t_{2,3} & & t_{2,64} \\ & \vdots & & \ddots & \vdots \\t_{16,1} & t_{16,2} & t_{16,3} & \ldots & t_{16,64}\end{bmatrix} \times \begin{bmatrix}r_{1} \\r_{2} \\ \vdots \\r_{64}\end{bmatrix}} & \left\lbrack {{Equation}5} \right\rbrack\end{matrix}$

In Equation 5, r₁ to r₆₄ may represent residual samples for the targetblock and may be specifically transform coefficients generated byapplying a primary transform. As a result of the calculation of Equation5 transform coefficients ci for the target block may be derived, and aprocess of deriving ci may be as in Equation 6.

for i from to R: [Equation 6]  c_(i)=0  for j from 1 to N   c_(i) +=t_(i,j) * r_(j)

As a result of the calculation of Equation 6, transform coefficients c₁to c_(R) for the target block may be derived. That is, when R=16,transform coefficients c₁ to c₁₆ for the target block may be derived.If, instead of RST, a regular transform is applied and a transformmatrix of 64×64 (N×N) size is multiplied to residual samples of 64×1(N×1) size, then only 16 (R) transform coefficients are derived for thetarget block because RST was applied, although 64 (N) transformcoefficients are derived for the target block. Since the total number oftransform coefficients for the target block is reduced from N to R, theamount of data transmitted by the encoding apparatus 200 to the decodingapparatus 300 decreases, so efficiency of transmission between theencoding apparatus 200 and the decoding apparatus 300 can be improved.

When considered from the viewpoint of the size of the transform matrix,the size of the regular transform matrix is 64×64 (N×N), but the size ofthe reduced transform matrix is reduced to 16×64 (R×N), so memory usagein a case of performing the RST can be reduced by an R/N ratio whencompared with a case of performing the regular transform. In addition,when compared to the number of multiplication calculations N×N in a caseof using the regular transform matrix, the use of the reduced transformmatrix can reduce the number of multiplication calculations by the R/Nratio (R×N).

In an example, the transformer 232 of the encoding apparatus 200 mayderive transform coefficients for the target block by performing theprimary transform and the RST-based secondary transform on residualsamples for the target block. These transform coefficients may betransferred to the inverse transformer of the decoding apparatus 300,and the inverse transformer 322 of the decoding apparatus 300 may derivethe modified transform coefficients based on the inverse reducedsecondary transform (RST) for the transform coefficients, and may deriveresidual samples for the target block based on the inverse primarytransform for the modified transform coefficients.

The size of the inverse RST matrix TN×R according to an example is N×Rless than the size N×N of the regular inverse transform matrix, and isin a transpose relationship with the reduced transform matrix T_(R×N)shown in Equation 4.

The matrix T^(t) in the Reduced Inv. Transform block shown in (b) ofFIG. 6 may mean the inverse RST matrix T_(R×N) ^(T) (the superscript Tmeans transpose). When the inverse RST matrix T_(R×N) ^(T) is multipliedto the transform coefficients for the target block as shown in (b) ofFIG. 6 , the modified transform coefficients for the target block or theresidual samples for the current block may be derived. The inverse RSTmatrix T_(R×N) ^(T) may be expressed as (T_(R×N)) T_(N×R).

More specifically, when the inverse RST is applied as the secondaryinverse transform, the modified transform coefficients for the targetblock may be derived when the inverse RST matrix TR×NT is multiplied tothe transform coefficients for the target block. Meanwhile, the inverseRST may be applied as the inverse primary transform, and in this case,the residual samples for the target block may be derived when theinverse RST matrix T_(R×N) ^(T) is multiplied to the transformcoefficients for the target block.

In an example, if the size of the block to which the inverse transformis applied is 8×8 and R=16 (i.e., R/N=16/64=¼), then the RST accordingto FIG. 6(b) may be expressed as a matrix operation as shown in Equation7 below.

$\begin{matrix}{\begin{bmatrix}t_{1,1} & t_{2,1} & & t_{16,1} \\t_{1,2} & t_{2,2} & \ldots & t_{16,2} \\t_{1,3} & t_{2,3} & & t_{16,3} \\ \vdots & \vdots & & \vdots \\ & \vdots & \ddots & \vdots \\t_{1,64} & t_{2,64} & \ldots & t_{16,64}\end{bmatrix} \times \begin{bmatrix}c_{1} \\c_{2} \\ \vdots \\c_{16}\end{bmatrix}} & \left\lbrack {{Equation}7} \right\rbrack\end{matrix}$

In Equation 7, c₁ to c₁₆ may represent the transform coefficients forthe target block. As a result of the calculation of Equation 7, r_(i)representing the modified transform coefficients for the target block orthe residual samples for the target block may be derived, and theprocess of deriving r_(i) may be as in Equation 8.

For i from 1 to N [Equation 8]  r_(i)=0   for j from 1 to R    r_(i)+=t_(ji) * c_(j)

As a result of the calculation of Equation 8, r₁ to r_(N) representingthe modified transform coefficients for the target block or the residualsamples for the target block may be derived. When considered from theviewpoint of the size of the inverse transform matrix, the size of theregular inverse transform matrix is 64×64 (N×N), but the size of thereduced inverse transform matrix is reduced to 64×16 (R×N), so memoryusage in a case of performing the inverse RST can be reduced by an R/Nratio when compared with a case of performing the regular inversetransform. In addition, when compared to the number of multiplicationcalculations N×N in a case of using the regular inverse transformmatrix, the use of the reduced inverse transform matrix can reduce thenumber of multiplication calculations by the R/N ratio (N×R).

A transform set configuration shown in Table 2 may also be applied to an8×8 RST. That is, the 8×8 RST may be applied according to a transformset in Table 2. Since one transform set includes two or three transforms(kernels) according to an intra prediction mode, it may be configured toselect one of up to four transforms including that in a case where nosecondary transform is applied. In a transform where no secondarytransform is applied, it may be considered to apply an identity matrix.Assuming that indexes 0, 1, 2, and 3 are respectively assigned to thefour transforms (e.g., index 0 may be allocated to a case where anidentity matrix is applied, that is, a case where no secondary transformis applied), a transform index or an lfnst index as a syntax element maybe signaled for each transform coefficient block, thereby designating atransform to be applied. That is, for a top-left 8×8 block, through thetransform index, it is possible to designate an 8×8 RST in an RSTconfiguration, or to designate an 8×8 lfnst when the LFNST is applied.The 8×8 lfnst and the 8×8 RST refer to transforms applicable to an 8×8region included in the transform coefficient block when both W and H ofthe target block to be transformed are equal to or greater than 8, andthe 8×8 region may be a top-left 8×8 region in the transform coefficientblock. Similarly, a 4×4 lfnst and a 4×4 RST refer to transformsapplicable to a 4×4 region included in the transform coefficient blockwhen both W and H of the target block to are equal to or greater than 4,and the 4×4 region may be a top-left 4×4 region in the transformcoefficient block.

According to an embodiment of the present disclosure, for a transform inan encoding process, only 48 pieces of data may be selected and amaximum 16×48 transform kernel matrix may be applied thereto, ratherthan applying a 16×64 transform kernel matrix to 64 pieces of dataforming an 8×8 region. Here, “maximum” means that m has a maximum valueof 16 in an m×48 transform kernel matrix for generating m coefficients.That is, when an RST is performed by applying an m×48 transform kernelmatrix (m≤16) to an 8×8 region, 48 pieces of data are input and mcoefficients are generated. When m is 16, 48 pieces of data are inputand 16 coefficients are generated. That is, assuming that 48 pieces ofdata form a 48×1 vector, a 16×48 matrix and a 48×1 vector aresequentially multiplied, thereby generating a 16×1 vector. Here, the 48pieces of data forming the 8×8 region may be properly arranged, therebyforming the 48×1 vector. For example, a 48×1 vector may be constructedbased on 48 pieces of data constituting a region excluding the bottomright 4×4 region among the 8×8 regions. Here, when a matrix operation isperformed by applying a maximum 16×48 transform kernel matrix, 16modified transform coefficients are generated, and the 16 modifiedtransform coefficients may be arranged in a top-left 4×4 regionaccording to a scanning order, and a top-right 4×4 region and abottom-left 4×4 region may be filled with zeros.

For an inverse transform in a decoding process, the transposed matrix ofthe foregoing transform kernel matrix may be used. That is, when aninverse RST or LFNST is performed in the inverse transform processperformed by the decoding apparatus, input coefficient data to which theinverse RST is applied is configured in a one-dimensional vectoraccording to a predetermined arrangement order, and a modifiedcoefficient vector obtained by multiplying the one-dimensional vectorand a corresponding inverse RST matrix on the left of theone-dimensional vector may be arranged in a two-dimensional blockaccording to a predetermined arrangement order.

In summary, in the transform process, when an RST or LFNST is applied toan 8×8 region, a matrix operation of 48 transform coefficients intop-left, top-right, and bottom-left regions of the 8×8 region excludingthe bottom-right region among transform coefficients in the 8×8 regionand a 16×48 transform kernel matrix. For the matrix operation, the 48transform coefficients are input in a one-dimensional array. When thematrix operation is performed, 16 modified transform coefficients arederived, and the modified transform coefficients may be arranged in thetop-left region of the 8×8 region.

On the contrary, in the inverse transform process, when an inverse RSTor LFNST is applied to an 8×8 region, 16 transform coefficientscorresponding to a top-left region of the 8×8 region among transformcoefficients in the 8×8 region may be input in a one-dimensional arrayaccording to a scanning order and may be subjected to a matrix operationwith a 48×16 transform kernel matrix. That is, the matrix operation maybe expressed as (48×16 matrix)*(16×1 transform coefficient vector)=(48×1modified transform coefficient vector). Here, an n×1 vector may beinterpreted to have the same meaning as an n×1 matrix and may thus beexpressed as an n×1 column vector. Further, * denotes matrixmultiplication. When the matrix operation is performed, 48 modifiedtransform coefficients may be derived, and the 48 modified transformcoefficients may be arranged in top-left, top-right, and bottom-leftregions of the 8×8 region excluding a bottom-right region.

When a secondary inverse transform is based on an RST, the inversetransformer 235 of the encoding apparatus 200 and the inversetransformer 322 of the decoding apparatus 300 may include an inversereduced secondary transformer to derive modified transform coefficientsbased on an inverse RST on transform coefficients and an inverse primarytransformer to derive residual samples for the target block based on aninverse primary transform for the modified transform coefficients. Theinverse primary transform refers to the inverse transform of a primarytransform applied to a residual. In the present disclosure, deriving atransform coefficient based on a transform may refer to deriving thetransform coefficient by applying the transform.

The above-described non-separated transform, the LFNST, will bedescribed in detail as follows. The LFNST may include a forwardtransform by the encoding apparatus and an inverse transform by thedecoding apparatus.

The encoding apparatus receives a result (or a part of a result) derivedafter applying a primary (core) transform as an input, and applies aforward secondary transform (secondary transform).

y=G ^(T) x  [Equation 9]

In Equation 9, x and y are inputs and outputs of the secondarytransform, respectively, and G is a matrix representing the secondarytransform, and transform basis vectors are composed of column vectors.In the case of an inverse LFNST, when the dimension of thetransformation matrix G is expressed as [number of rows×number ofcolumns], in the case of an forward LFNST, the transposition of matrix Gbecomes the dimension of G^(T).

For the inverse LFNST, the dimensions of matrix G are [48×16], [48×8],[16×16], [16×8], and the [48×8] matrix and the [16×8] matrix are partialmatrices that sampled 8 transform basis vectors from the left of the[48×16] matrix and the [16×16] matrix, respectively.

On the other hand, for the forward LFNST, the dimensions of matrix G^(T)are [16×48], [8×48], [16×16], [8×16], and the [8×48] matrix and the[8×16] matrix are partial matrices obtained by sampling 8 transformbasis vectors from the top of the [16×48] matrix and the [16×16] matrix,respectively.

Therefore, in the case of the forward LFNST, a [48×1] vector or [16×1]vector is possible as an input x, and a [16×1] vector or a [8×1] vectoris possible as an output y. In video coding and decoding, the output ofthe forward primary transform is two-dimensional (2D) data, so toconstruct the [48×1] vector or the [16×1] vector as the input x, aone-dimensional vector must be constructed by properly arranging the 2Ddata that is the output of the forward transformation.

FIG. 7 is a diagram illustrating a sequence of arranging output data ofa forward primary transformation into a one-dimensional vector accordingto an example. The left diagrams of (a) and (b) of FIG. 7 show thesequence for constructing a [48×1] vector, and the right diagrams of (a)and (b) of FIG. 7 shows the sequence for constructing a [16×1] vector.In the case of the LFNST, a one-dimensional vector x can be obtained bysequentially arranging 2D data in the same order as in (a) and (b) ofFIG. 7 .

The arrangement direction of the output data of the forward primarytransform may be determined according to an intra prediction mode of thecurrent block. For example, when the intra prediction mode of thecurrent block is in the horizontal direction with respect to thediagonal direction, the output data of the forward primary transform maybe arranged in the order of (a) of FIG. 7 , and when the intraprediction mode of the current block is in the vertical direction withrespect to the diagonal direction, the output data of the forwardprimary transform may be arranged in the order of (b) of FIG. 7 .

According to an example, an arrangement order different from thearrangement orders of (a) and (b) FIG. 7 may be applied, and in order toderive the same result (y vector) as when the arrangement orders of (a)and (b) FIG. 7 is applied, the column vectors of the matrix G may berearranged according to the arrangement order. That is, it is possibleto rearrange the column vectors of G so that each element constitutingthe x vector is always multiplied by the same transform basis vector.

Since the output y derived through Equation 9 is a one-dimensionalvector, when two-dimensional data is required as input data in theprocess of using the result of the forward secondary transformation asan input, for example, in the process of performing quantization orresidual coding, the output y vector of Equation 9 must be properlyarranged as 2D data again.

FIG. 8 is a diagram illustrating a sequence of arranging output data ofa forward secondary transform into a two-dimensional block according toan example.

In the case of the LFNST, output values may be arranged in a 2D blockaccording to a predetermined scan order. (a) of FIG. 8 shows that whenthe output y is a [16×1] vector, the output values are arranged at 16positions of the 2D block according to a diagonal scan order. (b) ofFIG. 8 shows that when the output y is a [8×1] vector, the output valuesare arranged at 8 positions of the 2D block according to the diagonalscan order, and the remaining 8 positions are filled with zeros. X in(b) of FIG. 8 indicates that it is filled with zero.

According to another example, since the order in which the output vectory is processed in performing quantization or residual coding may bepreset, the output vector y may not be arranged in the 2D block as shownin FIG. 8 . However, in the case of the residual coding, data coding maybe performed in 2D block (eg, 4×4) units such as CG (Coefficient Group),and in this case, the data are arranged according to a specific order asin the diagonal scan order of FIG. 8 .

Meanwhile, the decoding apparatus may configure the one-dimensionalinput vector y by arranging two-dimensional data output through adequantization process or the like according to a preset scan order forthe inverse transformation. The input vector y may be output as theoutput vector x by the following equation.

x=Gy  [Equation 10]

In the case of the inverse LFNST, an output vector x can be derived bymultiplying an input vector y, which is a [16×1] vector or a [8×1]vector, by a G matrix. For the inverse LFNST, the output vector x can beeither a [48×1] vector or a [16×1] vector.

The output vector x is arranged in a two-dimensional block according tothe order shown in FIG. 7 and is arranged as two-dimensional data, andthis two-dimensional data becomes input data (or a part of input data)of the inverse primary transformation.

Accordingly, the inverse secondary transformation is the opposite of theforward secondary transformation process as a whole, and in the case ofthe inverse transformation, unlike in the forward direction, the inversesecondary transformation is first applied, and then the inverse primarytransformation is applied.

In the inverse LFNST, one of 8 [48×16] matrices and 8 [16×16] matricesmay be selected as the transformation matrix G. Whether to apply the[48×16] matrix or the [16×16] matrix depends on the size and shape ofthe block.

In addition, 8 matrices may be derived from four transform sets as shownin Table 2 above, and each transform set may consist of two matrices.Which transform set to use among the 4 transform sets is determinedaccording to the intra prediction mode, and more specifically, thetransform set is determined based on the value of the intra predictionmode extended by considering the Wide Angle Intra Prediction (WAIP).Which matrix to select from among the two matrices constituting theselected transform set is derived through index signaling. Morespecifically, 0, 1, and 2 are possible as the transmitted index value, 0may indicate that the LFNST is not applied, and 1 and 2 may indicate anyone of two transform matrices constituting a transform set selectedbased on the intra prediction mode value.

FIG. 9 is a diagram illustrating wide-angle intra prediction modesaccording to an embodiment of the present document.

The general intra prediction mode value may have values from 0 to 66 and81 to 83, and the intra prediction mode value extended due to WAIP mayhave a value from −14 to 83 as shown. Values from 81 to 83 indicate theCCLM (Cross Component Linear Model) mode, and values from −14 to −1 andvalues from 67 to 80 indicate the intra prediction mode extended due tothe WAIP application.

When the width of the prediction current block is greater than theheight, the upper reference pixels are generally closer to positionsinside the block to be predicted. Therefore, it may be more accurate topredict in the bottom-left direction than in the top-right direction.Conversely, when the height of the block is greater than the width, theleft reference pixels are generally close to positions inside the blockto be predicted. Therefore, it may be more accurate to predict in thetop-right direction than in the bottom-left direction. Therefore, it maybe advantageous to apply remapping, ie, mode index modification, to theindex of the wide-angle intra prediction mode.

When the wide-angle intra prediction is applied, information on theexisting intra prediction may be signaled, and after the information isparsed, the information may be remapped to the index of the wide-angleintra prediction mode. Therefore, the total number of the intraprediction modes for a specific block (eg, a non-square block of aspecific size) may not change, and that is, the total number of theintra prediction modes is 67, and intra prediction mode coding for thespecific block may not be changed.

Table 3 below shows a process of deriving a modified intra mode byremapping the intra prediction mode to the wide-angle intra predictionmode.

TABLE 3 Inputs to this process are: - a variable predModeIntraspecifying the intra prediction mode, - a variable nTbW specifying thetransform block width, - a variable nTbH specifying the transform blockheight, - a variable cIdx specifying the colour component of the currentblock. Output of this process is the modified intra prediction modepredModeIntra. The variables nW and nH are derived as follows: - IfIntraSubPartitionsSplitType is equal to ISP_NO_SPLIT or cIdx is notequal to 0, the following applies:  nW = nTbW (8-97)  nH = nTbH (8-98) -Otherwise ( IntraSubPartitionsSplitType is set equal to ISP_NO_SPLIT andcIdx is equal to 0 ), the following applies:  nW = nCbW (8-99)  nH =nCbH (8-100) The variable whRatio is set equal to Abs( Log2( nW / nH )). For non-square blocks (nW is not equal to nH), the intra predictionmode predModeIntra is modified as follows: - If all of the followingconditions are true, predModeIntra is set equal to ( predModeIntra + 65). - nW is greater than nH - predModeIntra is greater than or equal to 2- predModeIntra is less than ( whRatio > 1 ) ? ( 8 + 2 * whRatio ) : 8 -Otherwise, if all of the following conditions are true, predModeIntra isset equal to ( predModeIntra − 67 ). - nH is greater than nW- predModeIntra is less than or equal to 66 - predModeIntra is greaterthan ( whRatio > 1 ) ?   ( 60 − 2 * whRatio ) : 60

In Table 3, the extended intra prediction mode value is finally storedin the predModeIntra variable, and ISP_NO_SPLIT indicates that the CUblock is not divided into sub-partitions by the Intra Sub Partitions(ISP) technique currently adopted in the VVC standard, and the cIdxvariable Values of 0, 1, and 2 indicate the case of luma, Cb, and Crcomponents, respectively. Log 2 function shown in Table 3 returns a logvalue with a base of 2, and the Abs function returns an absolute value.

Variable predModeIntra indicating the intra prediction mode and theheight and width of the transform block, etc. are used as input valuesof the wide angle intra prediction mode mapping process, and the outputvalue is the modified intra prediction mode predModeIntra. The heightand width of the transform block or the coding block may be the heightand width of the current block for remapping of the intra predictionmode. At this time, the variable whRatio reflecting the ratio of thewidth to the width may be set to Abs(Log 2(nW/nH)).

For a non-square block, the intra prediction mode may be divided intotwo cases and modified.

First, if all conditions (1)˜(3) are satisfied, (1) the width of thecurrent block is greater than the height, (2) the intra prediction modebefore modifying is equal to or greater than 2, (3) the intra predictionmode is less than the value derived from (8+2*whRatio) when the variablewhRatio is greater than 1, and is less than 8 when the variable whRatiois less than or equal to 1 [predModeIntra is less than (whRatio >1)?(8+2*whRatio): 8], the intra prediction mode is set to a value 65greater than the intra prediction mode [predModeIntra is set equal to(predModeIntra+65)].

If different from the above, that is, follow conditions (1)˜(3) aresatisfied, (1) the height of the current block is greater than thewidth, (2) the intra prediction mode before modifying is less than orequal to 66, (3) the intra prediction mode is greater than the valuederived from (60-2*whRatio) when the variable whRatio is greater than 1,and is greater than 60 when the variable whRatio is less than or equalto 1 [predModeIntra is greater than (whRatio >1)?(60-2*whRatio): 60],the intra prediction mode is set to a value 67 smaller than the intraprediction mode [predModeIntra is set equal to (predModeIntra−67)].

Table 2 above shows how a transform set is selected based on the intraprediction mode value extended by the WAIP in the LFNST. As shown inFIG. 9 , modes 14 to 33 and modes 35 to 80 are symmetric with respect tothe prediction direction around mode 34. For example, mode 14 and mode54 are symmetric with respect to the direction corresponding to mode 34.Therefore, the same transform set is applied to modes located inmutually symmetrical directions, and this symmetry is also reflected inTable 2.

Meanwhile, it is assumed that forward LFNST input data for mode 54 issymmetrical with the forward LFNST input data for mode 14. For example,for mode 14 and mode 54, the two-dimensional data is rearranged intoone-dimensional data according to the arrangement order shown in (a) ofFIG. 7 and (b) of FIG. 7 , respectively. In addition, it can be seenthat the patterns in the order shown in (a) of FIG. 7 and (b) of FIG. 7are symmetrical with respect to the direction (diagonal direction)indicated by Mode 34.

Meanwhile, as described above, which transform matrix of the [48×16]matrix and the [16×16] matrix is applied to the LFNST is determined bythe size and shape of the transform target block.

FIG. 10 is a diagram illustrating a block shape to which the LFNST isapplied. (a) of FIG. 10 shows 4×4 blocks, (b) shows 4×8 and 8×4 blocks,(c) shows 4×N or N×4 blocks in which N is 16 or more, (d) shows 8×8blocks, (e) shows M×N blocks where M≥8, N≥8, and N>8 or M>8.

In FIG. 10 , blocks with thick borders indicate regions to which theLFNST is applied. For the blocks of (a) and (b) of FIG. 10 , the LFNSTis applied to the top-left 4×4 region, and for the block of (c) of FIG.10 , the LFNST is applied individually the two top-left 4×4 regions arecontinuously arranged. In (a), (b), and (c) of FIG. 10 , since the LFNSTis applied in units of 4×4 regions, this LFNST will be hereinafterreferred to as “4×4 LFNST”. Based on the matrix dimension for G, a[16×16] or [16×8] matrix may be applied.

More specifically, the [16×8] matrix is applied to the 4×4 block (4×4 TUor 4×4 CU) of (a) of FIG. 10 and the [16×16] matrix is applied to theblocks in (b) and (c) of FIG. 10 . This is to adjust the computationalcomplexity for the worst case to 8 multiplications per sample.

With respect to (d) and (e) of FIG. 10 , the LFNST is applied to thetop-left 8×8 region, and this LFNST is hereinafter referred to as “8×8LFNST”. As a corresponding transformation matrix, a [48×16] matrix or[48×8] matrix may be applied. In the case of the forward LFNST, sincethe [48×1] vector (x vector in Equation 9) is input as input data, allsample values of the top-left 8×8 region are not used as input values ofthe forward LFNST. That is, as can be seen in the left order of (a) ofFIG. 7 or the left order of (b) of FIG. 7 , the [48×1] vector may beconstructed based on samples belonging to the remaining 3 4×4 blockswhile leaving the bottom-right 4×4 block as it is.

The [48×8] matrix may be applied to an 8×8 block (8×8 TU or 8×8 CU) in(d) of FIG. 10 , and the [48×16] matrix may be applied to the 8×8 blockin (e) of FIG. 10 . This is also to adjust the computational complexityfor the worst case to 8 multiplications per sample.

Depending on the block shape, when the corresponding forward LFNST (4×4LFNST or 8×8 LFNST) is applied, 8 or 16 output data (y vector inEquation 9, [8×1] or [16×1] vector) is generated. In the forward LFNST,the number of output data is equal to or less than the number of inputdata due to the characteristics of the matrix G^(T).

FIG. 11 is a diagram illustrating an arrangement of output data of aforward LFNST according to an example, and shows a block in which outputdata of the forward LFNST is arranged according to a block shape.

The shaded area at the top-left of the block shown in FIG. 11corresponds to the area where the output data of the forward LFNST islocated, the positions marked with 0 indicate samples filled with avalue of 0, and the remaining area represents regions that are notchanged by the forward LFNST. In the area not changed by the LFNST, theoutput data of the forward primary transform remains unchanged.

As described above, since the dimension of the transform matrix appliedvaries according to the shape of the block, the number of output dataalso varies. As FIG. 11 , the output data of the forward LFNST may notcompletely fill the top-left 4×4 block. In the case of (a) and (d) ofFIG. 11 , a [16×8] matrix and a [48×8] matrix are applied to the blockindicated by a thick line or a partial region inside the block,respectively, and a [8×1] vector as the output of the forward LFNST isgenerated. That is, according to the scan order shown in (b) of FIG. 8 ,only 8 output data may be filled as shown in (a) and (d) of FIGS. 11 ,and 0 may be filled in the remaining 8 positions. In the case of theLFNST applied block of (d) of FIG. 10 , as shown in (d) of FIG. 11 , two4×4 blocks in the top-right and bottom-left adjacent to the top-left 4×4block are also filled with a value of 0.

As described above, basically, by signaling the LFNST index, whether toapply the LFNST and the transform matrix to be applied are specified. Asshown FIG. 11 , when the LFNST is applied, since the number of outputdata of the forward LFNST may be equal to or less than the number ofinput data, a region filled with a zero value occurs as follows.

1) As shown in (a) of FIG. 11 , samples from the 8th and later positionsin the scan order in the top-left 4×4 block, that is, samples from the9th to the 16th.

2) As shown in (d) and (e) of FIG. 11 , when the [48×16] matrix or the[48×8] matrix is applied, two 4×4 blocks adjacent to the top-left 4×4block or the second and third 4×4 blocks in the scan order.

Therefore, if non-zero data exists by checking the areas 1) and 2), itis certain that the LFNST is not applied, so that the signaling of thecorresponding LFNST index can be omitted.

According to an example, for example, in the case of LFNST adopted inthe VVC standard, since signaling of the LFNST index is performed afterthe residual coding, the encoding apparatus may know whether there isthe non-zero data (significant coefficients) for all positions withinthe TU or CU block through the residual coding. Accordingly, theencoding apparatus may determine whether to perform signaling on theLFNST index based on the existence of the non-zero data, and thedecoding apparatus may determine whether the LFNST index is parsed. Whenthe non-zero data does not exist in the area designated in 1) and 2)above, signaling of the LFNST index is performed.

Since a runcated unary code is applied as a binarization method for theLFNST index, the LFNST index is composed of up to two bins. 0, 10, and11 are allocated as binary codes for possible LFNST index values of 0,1, and 2, respectively. According to an example, context-based CABACcoding may be applied to the first bin (regular coding), andcontext-based CABAC coding may be applied to the second bin as well. Thecoding of the LFNST index is shown in a table as follows

TABLE 4 binIdx Syntax element 0 1 2 3 4 >=5 . . . . . . . . . . . . . .. . . . . . . lfnst_idx[ ][ ] (treeType != 2 na na na na SINGLE_TREE) ?1:0 . . . . . . . . . . . . . . . . . . . . .

As shown in Table 4, for the first bin (binIdx=0), context No. 0 isapplied in the case of a single tree, and context No. 1 may be appliedin the case of a non-single tree. Also, as shown in Table 4, context No.2 may be applied to the second bin (binIdx=1). That is, two contexts maybe allocated to the first bin, one context may be allocated to thesecond bin, and each context may be distinguished by a ctxInc value (0,1, 2).

Here, the single tree means that the luma component and the chromacomponent are coded with the same coding structure. When the coding unitis split while having the same coding structure, and the size of thecoding unit becomes less than or equal to a specific threshold and theluma component and chroma component are coded with separate treestructures, the coding unit is regarded as a dual tree and the first bincontext may be determined. That is, as shown in Table 4, context No. 1may be allocated.

Alternatively, when the value of the variable treeType is allocated tothe first bin as SINGLE_TREE, context 0 may be used, otherwise context 1may be used for coding.

Meanwhile, for the adopted LFNST, the following simplification methodsmay be applied.

(i) According to an example, the number of output data for the forwardLFNST may be limited to a maximum of 16.

In the case of (c) of FIG. 10 , the 4×4 LFNST may be applied to two 4×4regions adjacent to the top-left, respectively, and in this case, amaximum of 32 LFNST output data may be generated. when the number ofoutput data for forward LFNST is limited to a maximum of 16, in the caseof 4×N/N×4 (N>16) blocks (TU or CU), the 4×4 LFNST is only applied toone 4×4 region in the top-left, the LFNST may be applied only once toall blocks of FIG. 10 . Through this, the implementation of image codingmay be simplified.

FIG. 12 shows that the number of output data for the forward LFNST islimited to a maximum of 16 according to an example. As FIG. 12 , whenthe LFNST is applied to the most top-left 4×4 region in a 4×N or N×4block in which N is 16 or more, the output data of the forward LFNSTbecomes 16 pieces.

(ii) According to an example, zero-out may be additionally applied to aregion to which the LFNST is not applied. In this document, the zero-outmay mean filling values of all positions belonging to a specific regionwith a value of 0. That is, the zero-out can be applied to a region thatis not changed due to the LFNST and maintains the result of the forwardprimary transformation. As described above, since the LFNST is dividedinto the 4×4 LFNST and the 8×8 LFNST, the zero-out can be divided intotwo types ((ii)-(A) and (ii)-(B)) as follows.

(ii)-(A) When the 4×4 LFNST is applied, a region to which the 4×4 LFNSTis not applied may be zeroed out. FIG. 13 is a diagram illustrating thezero-out in a block to which the 4×4 LFNST is applied according to anexample.

As shown in FIG. 13 , with respect to a block to which the 4×4 LFNST isapplied, that is, for all of the blocks in (a), (b) and (c) of FIG. 11 ,the whole region to which the LFNST is not applied may be filled withzeros.

On the other hand, (d) of FIG. 13 shows that when the maximum value ofthe number of the output data of the forward LFNST is limited to 16 asshown in FIG. 12 , the zero-out is performed on the remaining blocks towhich the 4×4 LFNST is not applied.

(ii)-(B) When the 8×8 LFNST is applied, a region to which the 8×8 LFNSTis not applied may be zeroed out. FIG. 14 is a diagram illustrating thezero-out in a block to which the 8×8 LFNST is applied according to anexample.

As shown in FIG. 14 , with respect to a block to which the 8×8 LFNST isapplied, that is, for all of the blocks in (d) and (e) of FIG. 11 , thewhole region to which the LFNST is not applied may be filled with zeros.

(iii) Due to the zero-out presented in (ii) above, the area filled withzeros may be not same when the LFNST is applied. Accordingly, it ispossible to check whether the non-zero data exists according to thezero-out proposed in (ii) over a wider area than the case of the LFNSTof FIG. 11 .

For example, when (ii)-(B) is applied, after checking whether thenon-zero data exists where the area filled with zero values in (d) and(e) of FIG. 11 in addition to the area filled with 0 additionally inFIG. 14 , signaling for the LFNST index can be performed only when thenon-zero data does not exist.

Of course, even if the zero-out proposed in (ii) is applied, it ispossible to check whether the non-zero data exists in the same way asthe existing LFNST index signaling. That is, after checking whether thenon-zero data exists in the block filled with zeros in FIG. 11 , theLFNST index signaling may be applied. In this case, the encodingapparatus only performs the zero out and the decoding apparatus does notassume the zero out, that is, checking only whether the non-zero dataexists only in the area explicitly marked as 0 in FIG. 11 , may performthe LFNST index parsing.

Various embodiments in which combinations of the simplification methods((i), (ii)-(A), (ii)-(B), (iii)) for the LFNST are applied may bederived. Of course, the combinations of the above simplification methodsare not limited to the following an embodiment, and any combination maybe applied to the LFNST.

EMBODIMENT

-   -   Limit the number of output data for forward LFNST to a maximum        of 16→(i)    -   When the 4×4 LFNST is applied, all areas to which the 4×4 LFNST        is not applied are zero-out→(ii)-(A)    -   When the 8×8 LFNST is applied, all areas to which the 8×8 LFNST        is not applied are zero-out→(ii)-(B)    -   After checking whether the non-zero data exists also the        existing area filled with zero value and the area filled with        zeros due to additional zero outs ((ii)-(A), (ii)-(B)), the        LFNST index is signaled only when the non-zero data does not        exist→(iii)

In the case of the Embodiment, when the LFNST is applied, an area inwhich the non-zero output data can exist is limited to the inside of thetop-left 4×4 area. In more detail, in the case of (a) of FIG. 13 and (a)of FIG. 14 , the 8th position in the scan order is the last positionwhere non-zero data can exist. In the case of (b) and (c) of FIG. 13 and(b) of FIG. 14 , the 16th position in the scan order (ie, the positionof the bottom-right edge of the top-left 4×4 block) is the last positionwhere data other than 0 may exist.

Therefore, when the LFNST is applied, after checking whether thenon-zero data exists in a position where the residual coding process isnot allowed (at a position beyond the last position), it can bedetermined whether the LFNST index is signaled.

In the case of the zero-out method proposed in (ii), since the number ofdata finally generated when both the primary transform and the LFNST areapplied, the amount of computation required to perform the entiretransformation process can be reduced. That is, when the LFNST isapplied, since zero-out is applied to the forward primary transformoutput data existing in a region to which the LFNST is not applied,there is no need to generate data for the region that become zero-outduring performing the forward primary transform. Accordingly, it ispossible to reduce the amount of computation required to generate thecorresponding data. The additional effects of the zero-out methodproposed in (ii) are summarized as follows.

First, as described above, the amount of computation required to performthe entire transform process is reduced.

In particular, when (ii)-(B) is applied, the amount of calculation forthe worst case is reduced, so that the transform process can belightened. In other words, in general, a large amount of computation isrequired to perform a large-size primary transformation. By applying(ii)-(B), the number of data derived as a result of performing theforward LFNST can be reduced to 16 or less. In addition, as the size ofthe entire block (TU or CU) increases, the effect of reducing the amountof transform operation is further increased.

Second, the amount of computation required for the entire transformprocess can be reduced, thereby reducing the power consumption requiredto perform the transform.

Third, the latency involved in the transform process is reduced.

The secondary transformation such as the LFNST adds a computationalamount to the existing primary transformation, thus increasing theoverall delay time involved in performing the transformation. Inparticular, in the case of intra prediction, since reconstructed data ofneighboring blocks is used in the prediction process, during encoding,an increase in latency due to a secondary transformation leads to anincrease in latency until reconstruction. This can lead to an increasein overall latency of intra prediction encoding.

However, if the zero-out suggested in (ii) is applied, the delay time ofperforming the primary transform can be greatly reduced when LFNST isapplied, the delay time for the entire transform is maintained orreduced, so that the encoding apparatus can be implemented more simply.

In the conventional intra prediction, a block to be currently encoded isregarded as one encoding unit and encoding was performed withoutsplitting. However, intra sub-partitions (ISP) coding means performingintra prediction encoding by dividing a block to be currently encoded ina horizontal direction or a vertical direction. In this case, areconstructed block may be generated by performing encoding/decoding inunits of divided blocks, and the reconstructed block may be used as areference block of the next divided block. According to an embodiment,in ISP coding, one coding block may be divided into two or foursub-blocks and coded, and in ISP, in one sub-block, intra prediction isperformed with reference to a reconstructed pixel value of a sub-blocklocated at the adjacent left side or adjacent upper side. Hereinafter,“coding” may be used as a concept including both coding performed by anencoding apparatus and decoding performed by a decoding apparatus.

Meanwhile, according to an embodiment, an LFNST index may be signaledfor each coding unit as shown below in the following table.

TABLE 5 Descriptor coding_unit( x0, y0, cbWidth, cbHeight, cqtDepth,treeType, modeType ) {   ......   LfnstDcOnly = 1  LfnstZeroOutSigCoeffFlag = 1   MtsZeroOutSigCoeffFlag = 1  transform_tree( x0, y0, cbWidth, cbHeight, treeType, chType )  lfnstWidth = ( treeType = = DUAL_TREE_CHROMA ) ? cbWidth / SubWidthC      : ( ( IntraSubPartitionsSplitType = = ISP_VER_SPLIT) ? cbWidth /       NumIntraSubPartitions : cbWidth )   lfnstHeight = ( treeType = =DUAL_TREE_CHROMA ) cbHeight / SubHeightC       : (IntraSubPartitionsSplitType = = ISP_HOR_SPLIT) ? cbHeight /       NumIntraSubPartitions : cbHeight )   if( Min( lfnstWidth,lfnstHeight ) >= 4 && sps_lfnst_enabled_flag = = 1 &&    CuPredMode[chType ][ x0 ][ y0 ] = = MODE_INTRA &&    transform_skip_flag[ x0 ][ y0] = = 0 &&    ( treeType = = DUAL_TREE_CHROMA | | !intra_mip_flag[ x0 ][y0 ] | |      Min( lfnstWidth, lfnstHeight ) >= 16 ) &&    Max( cbWidth,cbHeight ) <= MaxTbSizeY) {    if( ( IntraSubPartitionsSplitType !=ISP_NO_SPLIT | | LfnstDcOnly = = 0 ) &&     LfnstZeroOutSigCoeffFlag == 1 )     lfnst_idx ae(v)   }   if( treeType != DUAL_TREE_CHROMA &&lfnst_idx[ x0 ][ y0 ] = = 0 &&    transform_skip_flag[ x0 ][ y0 ][ 0 ] == 0 && Max( cbWidth, cbHeight ) <= 32 &&    IntraSubPartitionsSplit[ x0][ y0 ] = = ISP_NO_SPLIT && cu_sbt_flag = = 0 &&   MtsZeroOutSigCoeffFlag = = 1 && tu_cbf_luma[ x0 ][ y0 ] ) {    if( (( CuPredMode[ chType ][ x0 ][ y0 ] = = MODE_INTER &&    sps_explicit_mts_inter_enabled_flag ) | |     ( CuPredMode[ chType][ x0 ][ y0 ] = = MODE_INTRA &&     sps_explicit_mts_intra_enabled_flag) ) )     mts_idx ae(v)   }  }

The LFNST index (lfnst_idx) is signaled only when transform skip is notapplied to the luma component, as shown in Table 5. That is, this meansthat the LFNST index (lfnst_idx) is signaled only when the conditiontransform_skip_flag[x0][y0][0]==0 is satisfied. Herein, x0 and y0 mean(x0, y0) coordinates when the top-left position is (0, 0) in the picturefor the luma component, and the horizontal X coordinate increases fromleft to right, and the vertical Y coordinate increases from top tobottom.

Although (x0, y0) are coordinates that are based on the luma component,the coordinates may also be used for the chroma phase component. In thiscase, the actual position indicated by the (x0, y0) coordinates may bescaled based on the picture for the chroma component. For example, whenthe chroma format is 4:2:0, the actual position of the chroma componentwithin the picture that is indicated by (x0, y0) may be (x0/2, y0/2).Thereafter, x0 and y0 that are shown later on may be indicated based onthe luma component regardless of whether the component that is currentlybeing handled (or processed) is luma or chroma.

In transform_skip_flag[x0][y0][0], the last index 0 means the lumacomponent. More specifically, in transform_skip_flag[x0][y0][cIdx], cIdxindicates the color component, and, if the cIdx value is equal to 0,this indicates luma. And, if the cIdx value is greater than 0 (or equalto 1 or 2), this indicates chroma.

Additionally, the variable LfnstDcOnly is initialized to a value of 1,as shown in Table 5, and may be set to a value of 0 according to acondition in the parsing function for residual coding, as shown below inthe Table 6.

TABLE 6 Descriptor residual_coding( x0, y0, log2TbWidth, log2TbHeight,cIdx ) {  if( ( sps_mts_enabled_flag && cu_sbt_flag && cIdx = = 0 &&   log2TbWidth < 6 && log2TbHeight < 6 && log2TbWidth > 4 )  log2ZoTbWidth = 4  Else   log2ZoTbWidth = Min( log2TbWidth, 5 )  if(sps_mts_enabled_flag && cu_sbt_flag && cIdx = = 0 &&    log2TbWidth < 6&& log2TbHeight < 6 && log2TbHeight > 4 )   log2ZoTbHeight = 4  Else  log2ZoTbHeight = Min( log2TbHeight, 5 )  if( log2TbWidth > 0 )  last_sig_coeff_x_prefix ae(v)  if( log2TbHeight > 0 )  last_sig_coeff_y_prefix ae(v)  if( last_sig_coeff_x_prefix > 3 )  last_sig_coeff_x_suffix ae(v)  if( last_sig_coeff_y_prefix > 3 )  last_sig_coeff_y_suffix ae(v)  log2TbWidth = log2ZoTbWidth log2TbHeight = log2ZoTbHeight  remBinsPass1 = ( ( 1 << ( log2TbWidth +log2TbHeight ) ) * 7 ) >> 2  log2SbW = ( Min( log2TbWidth, log2TbHeight) < 2 ? 1 : 2 )  log2SbH = log2SbW  if( log2TbWidth + log2TbHeight > 3 ){   if( log2TbWidth < 2 ) {     log2SbW = log2TbWidth     log2SbH = 4 −log2SbW   } else if( log2TbHeight < 2 ) {     log2SbH = log2TbHeight    log2SbW = 4 − log2SbH   }  numSbCoeff = 1 << ( log2SbW + log2SbH ) lastScanPos = numSbCoeff  lastSubBlock = ( 1 << ( log2TbWidth +log2TbHeight − ( log2SbW + log2SbH ) ) ) − 1  do {   if( lastScanPos == 0 ) {     lastScanPos = numSbCoeff     lastSubBlock− −   }  lastScanPos− −   xS = DiagScanOrder[ log2TbWidth − log2SbW ][log2TbHeight − log2SbH ]      [ lastSubBlock ][ 0 ]   yS =DiagScanOrder[ log2TbWidth − log2SbW ][ log2TbHeight − log2SbH ]      [lastSubBlock ][ 1 ]   xC = ( xS << log2SbW ) + DiagScanOrder[ log2SbW ][log2SbH ][ lastScanPos ][ 0 ]   yC = ( yS << log2SbH ) + DiagScanOrder[log2SbW ][ log2SbH ][ lastScanPos ][ 1 ]  } while( ( xC !=LastSignificantCoeffX ) | | ( yC != LastSignificantCoeffY ) )  if(lastSubBlock = = 0 && log2TbWidth >= 2 && log2TbHeight >= 2 &&  !transform_skip_flag[ x0 ][ y0 ][ cIdx ] && lastScanPos > 0 )  LfnstDcOnly = 0  if( ( lastSubBlock > 0 && log2TbWidth >= 2 &&log2TbHeight >= 2 ) | |   ( lastScanPos > 7 && ( log2TbWidth = = 2 | |log2TbWidth = = 3 ) &&   log2TbWidth = = log2TbHeight ) )  LfnstZeroOutSigCoeffFlag = 0  ...... }

As shown in Table 6, the LfnstDcOnly value may be set to 0 only when thetransform_skip_flag[x0][y0][cIdx] value is equal to 0 (i.e., only whenthe transform skip is not applied to the component indicated by cIdx).

Additionally, when the transform_skip[x0][y0][cIdx] value is equal to 1,as shown in Table 7, a transform skip residual coding(residual_ts_coding) function is called instead of a residual coding(residual_coding) function. According to an example, since a part thatconfigures the LfnstDcOnly variable value is not present in theresidual_ts_coding function, the LfnstDcOnly value may be set to 0 onlywhen the transform_skip_flag[x0][y0][cIdx] value is equal to 0.

Additionally, when the transform_skip[x0][y0][cIdx] value is equal to 1,as described above, since a residual_ts_coding function is calledinstead of a residual_coding function, under the condition of settingthe LfnstDcOnly variable of Table 6 to 0,!transform_skip_flag[x0][y0][cIdx] may be removed. That is, if(lastSubBlock==0 && log 2TbWidth >=2 && log 2TbHeight >=2 &&lastScanPos >0) may be set instead of if (lastSubBlock==0 && log2TbWidth >=2 && log 2TbHeight >=2 && !transform_skip_flag[x0][y0][cIdx]&& lastScanPos >0).

If the ISP mode is not applied, as shown in Table 5, the LFNST index issignaled only when the LfnstDCOnly value is equal to 0, and, when theLFNST index is not signaled, the LFNST index value may be inferred to beequal to 0.

The residual coding function presented in Table 6 is called whileperforming a transform tree (the transform_tree), which is called inTable 5. Herein, in case of a single tree, both the residual codingfunction for luma (cIdx=0) and the residual coding function for chroma(cIdx=1 or 2, corresponding to the Cb component and the Cr component)are called. And, in case of a dual tree, when the dual tree is a dualtree for luma (DUAL_TREE_LUMA), only the residual coding function forluma (cIdx=0) is called, and, when the dual tree is a dual tree forchroma (DUAL_TREE_CHROMA), only the residual coding function for chroma(cIdx=1 or 2, the Cb component and the Cr component) is called.

The conditions under which the LFNST index is signaled for the casewhere the ISP mode is not applied are summarized as follows (herein, itmay be assumed that other conditions for the LFNST index to be signaledare satisfied, e.g., it is assumed that the condition Max(cbWidth,cbHeight)<=MaxTbSizeY is satisfied).

1. When transform_skip_flag[x0][y0][0] is equal to 1

-   -   LFNST index is inferred to be equal to 0 without performing        signaling

2. When transform_skip_flag[x0][y0][0] is equal to 0

2-A. When transform_skip_flag[x0][y0][1] is equal to 0 andtransform_skip_flag[x0][y0][2] is equal to 0

-   -   LfnstDcOnly value may be set to 0 for all cIdx in Table 6 (for        cases where cIdx is equal to 0, 1, 2)    -   If the LfnstDcOnly value is equal to 0, the LFNST index is        signaled. Otherwise, the LFNST index is not signaled and the        value is inferred to be equal to 0.

2-B. When transform_skip_flag[x0][y0][1] is equal to 0 andtransform_skip_flag[x0][y0][2] is equal to 1

-   -   In Table 6, the LfnstDcOnly value can be set to 0 only when cIdx        is equal to 0 and 1    -   If the LfnstDcOnly value is equal to 0, the LFNST index is        signaled. Otherwise, the LFNST index is not signaled and the        value is inferred to be equal to 0.

2-C. When transform_skip_flag[x0][y0][1] is equal to 1 andtransform_skip_flag[x0][y0][2] is equal to 0

-   -   In Table 6, the LfnstDcOnly value may be set to 0 only when cIdx        is equal to 0 and 2.    -   If the LfnstDcOnly value is equal to 0, the LFNST index is        signaled. Otherwise, the LFNST index is not signaled and the        value is inferred to be equal to 0.

2-D. When transform_skip_flag[x0][y0][1] is equal to 1 andtransform_skip_flag[x0][y0][2] is equal to 1

-   -   In Table 6, the LfnstDcOnly value may be set to 0 only when cIdx        is equal to 0    -   If the LfnstDcOnly value is equal to 0, the LFNST index is        signaled. Otherwise, the LFNST index is not signaled and the        value is inferred to be equal to 0.

In case of the single tree, all of the transform_skip_flag[x0][y0][0],transform_skip_flag[x0][y0][1], transform_skip_flag[x0][y0][2] valuesare checked for the cases listed above, in case of the dual tree forluma, only transform_skip_flag[x0][y0][0] is checked, and in case of thedual tree for chroma, the values of transform_skip_flag[x0][y0][1] andtransform_skip_flag[x0][y0][2] are checked.

In case of the ISP mode (this means the IntraSubPartitionsSplitType!=ISP_NO_SPLIT condition in Table 5, i.e., horizontal division (orpartition) or vertical division), as shown in Table 5, the LFNST indexis signaled without checking the LfnstDcOnly variable. Therefore, incase of the ISP mode in the single tree and dual tree for luma,regardless of the value of LfnstDcOnly variable, whentransform_skip_flag[x0][y0][0] value is 0 (herein, the transform skip isnot applied for luma component), the LFNST index is signaled (when theLFNST index is not signaled, the LFNST index value may be inferred to beequal to 0).

According to an example, when the ISP prediction is applied only forluma and not applied for chroma, in case of the dual tree for chroma,the LfnstDcOnly variable is checked and then the LFNST index may besignaled, just as in the above-described method.

As shown in Table 6, the LfnstDcOnly variable may be set to 0 only forthe case where the transform_skip_flag[x0][y0][cIdx] value is equal to0.

According to an embodiment, when the application of the ISP mode to theluma component may even influence the case of the dual tree for chroma,for the dual tree chroma component, when thetransform_skip_flag[x0][y0][0] value is equal to 0 regardless of theLfnstDcOnly variable, the LFNST index may be signaled.

The conditions under which the LFNST index is signaled when the ISP modeis applied and the transform_skip_flag[x0][y0][0] value is equal to 0are summarized as follows. (If the transform_skip_flag[x0][y0][0] valueis equal to 1, the LFNST index is not signaled and is inferred to beequal to 0. In Table 5, it may be assumed that other conditions requiredfor signaling the LFNST index are satisfied, and, for example, thecondition such as Max(cbWidth, cbHeight)<=MaxTbSizeY may be satisfied).

1. In case of a single tree

-   -   LFNST index signaling is performed regardless of the LfnstDcOnly        variable value

2. In case of a dual tree

2-A. In case of a dual tree for luma

-   -   LFNST index signaling is performed regardless of the LfnstDcOnly        variable value

2-B. In case of a dual tree for chroma

-   -   According to the values of transform_skip_flag[x0][y0][1] and        transform_skip_flag[x0][y0][2], the LfnstDcOnly variable value        may be set to 0. That is, in transform_skip_flag[x0][y0][cIdx],        when the cIdx value is equal to 1, the LfnstDcOnly variable        value may be set to 0 only when the        transform_skip_flag[x0][y0][1] value is equal to 0, and, when        the cIdx value is equal to 2, the LfnstDcOnly variable value may        be set to 0 only when the transform_skip_flag[x0][y0][2] value        is equal to 0.    -   If the LfnstDcOnly value is equal to 0, the LFNST index is        signaled. Otherwise, the LFNST index is not signaled and the        value is inferred to be equal to 0.

In the above-described cases, the case of the dual tree for chroma isthe same as the case where the ISP is not applied.

According to an example, while the transform skip for a chroma componentis authorized (or allowed), a transform skip flag corresponding to eachchroma component may be added as shown below in Table 7.

TABLE 7 Descriptor transform_unit( x0, y0, tbWidth, tbHeight, treeType,subTuIndex, chType ) {   ......  if( tu_cbf_luma[ x0 ][ y0 ] && treeType!= DUAL_TREE_CHROMA ) {   if( sps_transform_skip_enabled_flag &&!BdpcmFlag[ x0 ][ y0 ][ 0 ] &&..    tbWidth <= MaxTsSize && tbHeight <=MaxTsSize &&    ( IntraSubPartitionsSplit[ x0 ][ y0 ] = = ISP_NO_SPLIT )&& !cu_sbt_flag )    transform_skip_flag[ x0 ][ y0 ][ 0 ] ae(v)   if(!transform_skip_flag[ x0 ][ y0 ][ 0 ] )    residual_coding( x0, y0,Log2( tbWidth ), Log2( tbHeight ), 0 )   Else    residual_ts_coding( x0,y0, Log2( tbWidth), Log2( tbHeight), 0 )  }  if( tu_cbf_cb[ xC ][ yC ]&& treeType != DUAL_TREE_LUMA ) {   if( sps_transform_skip_enabled_flag&& !BdpcmFlag[ x0 ][ y0 ][ 1 ] &&    wC <= MaxTsSize && hC <= MaxTsSize&& !cu_sbt_flag )    transform_skip_flag[ xC ][ yC ][ 1 ] ae(v)   if(!transform_skip_flag[ xC ][ yC ][ 1 ] )    residual_coding( xC, yC,Log2( wC ), Log2( hC ), 1 )   Else    residual_ts_coding( xC, yC, Log2(wC ), Log2( hC ), 1 )  }  if( tu_cbf_cr[ xC ][ yC ] && treeType !=DUAL_TREE_LUMA &&   !( tu_cbf_cb[ xC ][ yC ] &&tu_joint_cbcr_residual_flag[ xC ][ yC ] ) ) {   if(sps_transform_skip_enabled_flag && !BdpcmFlag[ x0 ][ y0 ][ 2 ] &&    wC<= MaxTsSize && hC <= MaxTsSize && !cu_sbt_flag )   transform_skip_flag[ xC ][ yC ][ 2 ] ae(v)   if(!transform_skip_flag[ xC ][ yC ][ 2 ] )    residual_coding( xC, yC,Log2( wC ), Log2( hC ), 2 )   Else    residual_ts_coding( xC, yC, Log2(wC ), Log2( hC ), 2 )  } }

As shown in Table 7, with the exception for the case where the dual treeis a dual tree for luma, the transform_skip_flag[xC][yC][1]corresponding to whether or not the transform skip is applied to Cb andthe transform_skip_flag[xC][yC][2] corresponding to whether or not thetransform skip is applied to Cr may be signaled.

If the transform_skip_flag[xC][yC][1] value is equal to 1, this meansthat the transform skip is applied to Cb, and if thetransform_skip_flag[xC][yC][1] value is equal to 0, this means that thetransform skip is not applied to Cb. And, if thetransform_skip_flag[xC][yC][2] value is equal to 1, this means that thetransform skip is applied to Cr, and if thetransform_skip_flag[xC][yC][2] value is equal to 0, the transform skipis not applied to Cr.

Therefore, even when the LFNST index value is greater than 0 (i.e., whenLFNST is applied), each transform_skip_flag[x0][y0][cIdx] value for theluma component (Y component) and the chroma component (Cb component andCr component) may be different. According to Table 5, since the LFNSTindex value may be greater than 0 only when thetransform_skip_flag[x0][y0][0] value is equal to 0, when the LFNST indexvalue is greater than 0, the transform_skip_flag[x0][y0][0] value isalways equal to 0.

Therefore, the cases where the LFNST may be applied according to thetransform_skip_flag[x0][y0][cIdx] value are summarized as follows.Herein, the LFNST index is greater than 0, and thetransform_skip_flag[x0][y0][0] value is equal to 0. It will be assumedthat other conditions for applying the LFNST are satisfied, for example,the condition of both the width and height of the corresponding blockbeing greater than or equal to 4 is satisfied.

1. Single tree type

-   -   LFNST is applied to luma component    -   If a transform_skip_flag[x0][y0][1] value is equal to 0, the        LFNST is applied to the Cb component, and, if the        transform_skip_flag[x0][y0][1] value is equal to 1, the LFNST is        not applied to the Cb component.    -   If a transform_skip_flag[x0][y0][2] value is equal to 0, the        LFNST is applied to the Cr component, and, if the        transform_skip_flag[x0][y0][2] value is equal to 1, the LFNST is        not applied to the Cr component.

2. Dual tree for luma

-   -   LFNST is applied to luma component

3. Dual tree for chroma

-   -   If the transform_skip_flag[x0][y0][1] value is equal to 0, the        LFNST is applied to the Cb component, and, if the        transform_skip_flag[x0][y0][1] value is equal to 1, the LFNST is        not applied to the Cb component.    -   If the transform_skip_flag[x0][y0][2] value is equal to 0, the        LFNST is applied to the Cr component, and, if the        transform_skip_flag[x0][y0][2] value is equal to 1, the LFNST is        not applied to the Cr component.

As described above, in order to selectively apply the LFNST according tothe transform_skip_flag[x0][y0][cIdx] value, the following conditionsshown below in Table 8 should be added to part corresponding to thespecification text for the LFNST.

TABLE 8 8.7.4 Transformation process for scaled transform coefficients8.7.4.1 General Inputs to this process are: - a luma location ( xTbY,yTbY ) specifying the top-left sample of the current luma transformblock relative to the top-left luma sample of the current picture, - avariable nTbW specifying the width of the current transform block, - avariable nTbH specifying the height of the current transform block, - avariable cIdx specifying the colour component of the current block, - an(nTbW)x(nTbH) array d[ x ][ y ] of scaled transform coefficients with x= 0..nTbW − 1, y = 0..nTbH − 1. Output of this process is the(nTbW)x(nTbH) array res[ x ][ y ] of residual samples with x = 0..nTbW −1, y = 0..nTbH − 1. When lfnst_idx is not equal to 0 andtransform_skip_flag[ xTbY ][ yTbY ][ cIdx ] is equal to 0 and both nTbWand nTbH are greater than or equal to 4, the following applies: - Thevariables predModeIntra, nLfnstOutSize, log2LfnstSize, nLfnstSize, andnonZeroSize are derived as follows:  predModeIntra =  ( cIdx = = 0 ) ?IntraPredModeY[ xTbY ][ yTbY ] : IntraPredModeC[ xTbY ][ yTbY ] (8-954) nLfnstOutSize = ( nTbW >= 8 && nTbH >= 8 ) ? 48 : 16 (8-955) log2LfnstSize = ( nTbW >= 8 && nTbH >= 8 ) ? 3 : 2 (8-956)  nLfnstSize= 1 << log2LfnstSize (8-957)  nonZeroSize = ( ( nTbW = = 4 && nTbH = = 4) | |  ( nTbW = = 8 && nTbH = = 8 ) ) ? 8 : 16 (8-958)

As shown in Table 8, when the LFNST index (lfnst_idx) value is not equalto 0 (i.e, when LFNST is applied), by checking thetransform_skip_flag[xTbY][yTbY][cIdx] value for the component designatedby cIdx (i.e., when lfnst_idx is not equal to 0), the LFNST may beconfigured to be applied only when thetransform_skip_flag[xTbY][yTbY][cIdx] value is equal to 0.

Meanwhile, according to an example, a method for signaling the LFNSTindex according to whether or not the transform is skipped for eachcolor component. In comparison to Table 5, as shown in Table 9, thecondition for transmitting the LFNST index can be removed only when thetransform_skip_flag[x0][y0][0] value is equal to 0.

TABLE 9 Descriptor coding_unit( x0, y0, cbWidth, cbHeight, cqtDepth,treeType, modeType ) {   ......   LfnstDcOnly = 1  LfnstZeroOutSigCoeffFlag = 1   MtsZeroOutSigCoeffFlag = 1  transform_tree( x0, y0, cbWidth, cbHeight, treeType, chType )  lfnstWidth = ( treeType = = DUAL_TREE_CHROMA ) ? cbWidth / SubWidthC      : ( ( IntraSubPartitionsSplitType = = ISP_VER_SPLIT ) ? cbWidth /       NumIntraSubPartitions : cbWidth )   lfnstHeight = ( treeType = =DUAL_TREE_CHROMA ) ? cbHeight / SubHeightC       : ( (IntraSubPartitionsSplitType = = ISP_HOR_SPLIT) ? cbHeight /       NumIntraSubPartitions : cbHeight )   if( Min( lfnstWidth,lfnstHeight ) >= 4 && sps_lfnst_enabled_flag = = 1 &&    CuPredMode[chType ][ x0 ][ y0 ] = = MODE_INTRA &&    ( treeType = =DUAL_TREE_CHROMA | | !intra_mip_flag[ x0 ][ y0 ] | |     Min(lfnstWidth, lfnstHeight ) >= 16 ) &&    Max( cbWidth, cbHeight) <=MaxTbSizeY) {    if( ( IntraSubPartitionsSplitType != ISP_NO_SPLIT | |LfnstDcOnly = = 0 ) &&     LfnstZeroOutSigCoeffFlag = = 1 )    lfnst_idx ae(v)   }   if( treeType != DUAL_TREE_CHROMA && lfnst_idx= = 0 &&    transform_skip_flag[ x0 ][ y0 ][ 0 ] = = 0 && Max( cbWidth,cbHeight ) <= 32 &&    IntraSubPartitionsSplit[ x0 ][ y0 ] = =ISP_NO_SPLIT && cu_sbt_flag = = 0 &&    MtsZeroOutSigCoeffFlag = = 1 &&tu_cbf_luma[ x0 ][ y0 ] ) {    if( ( ( CuPredMode[ chType ][ x0 ][ y0 ]= = MODE_INTER &&     sps_explicit_mts_inter_enabled_flag ) | |     (CuPredMode[ chType ][ x0 ][ y0 ] = = MODE_INTRA &&    sps_explicit_mts_intra_enabled_flag ) ) )     mts_idx ae(v)   }  }

However, since the method of configuring the LfnstDcOnly variable valuethat is included in Table 9 is the same as the method shown in Table 6,the configuration of the LfnstDcOnly variable value varies according tothe transform_skip_flag[x0][y0][cIdx] value, and, finally, whether ornot to perform signaling of the LFNST index may also vary (or change).

When the ISP mode is not applied, the method for signaling the LFNSTindex according to the transform_skip_flag[x0][y0][cIdx] value issummarized as follows. It may be assumed that other conditions forsignaling the LFNST index are already satisfied, for example, it will beassumed that a condition of Max(cbWidth, cbHeight)<=MaxTbSizeY issatisfied.

1. In case of a single tree

-   -   When the transform_skip_flag[x0][y0][0] value is equal to 0, the        LfnstDcOnly variable value may be set to 0 according to the        method proposed in Table 6.    -   When the transform_skip_flag[x0][y0][1] value is equal to 0, the        LfnstDcOnly variable value may be set to 0 according to the        method proposed in Table 6.    -   When the transform_skip_flag[x0][y0][2] value is equal to 0, the        LfnstDcOnly variable value may be set to 0 according to the        method proposed in Table 6.

When the LfnstDcOnly value is equal to 0, the LFNST index may besignaled. And, if the LFNST index is not signaled, the LfnstDcOnly valuemay be inferred to be equal to 0.

2. In case of a dual tree for luma component

-   -   When the transform_skip_flag[x0][y0][0] value is equal to 0, the        LfnstDcOnly variable value may be set to 0 according to the        method proposed in Table 6.    -   When the LfnstDcOnly value is equal to 0, the LFNST index may be        signaled. And, if the LFNST index is not signaled, the        LfnstDcOnly value may be inferred to be equal to 0.

3. In case of a dual tree for chroma component

-   -   When the transform_skip_flag[x0][y0][1] value is equal to 0, the        LfnstDcOnly variable value may be set to 0 according to the        method proposed in Table 6.    -   When the transform_skip_flag[x0][y0][2] value is equal to 0, the        LfnstDcOnly variable value may be set to 0 according to the        method proposed in Table 6.    -   When the LfnstDcOnly value is equal to 0, the LFNST index may be        signaled. And, if the LFNST index is not signaled, the        LfnstDcOnly value may be inferred to be equal to 0.

As shown in Table 9, the LfnstDcOnly value is initialized to 1, and, incase of the dual tree, the LFNST index corresponding to the dual treefor luma and the LFNST index corresponding to the dual tree for chromaare separately signaled. This means that different LFNST kernels may beapplied to each of the luma component and the chroma component.

The dual tree of the present disclosure includes DUAL_TREE_LUMA(corresponding to a luma component) and DUAL_TREE_CHROMA (correspondingto a chroma component). And, the dual tree may include a case where thedual tree is divided into a syntax parsing tree for luma and a syntaxparsing tree for chroma due to a coding unit size condition, or thelike, e.g., separate trees.

When the ISP mode is applied, as shown in Table 7, thetransform_skip_flag[x0][y0][0] is not signaled and is inferred to beequal to 0. That is, as shown in Table 7, transform_skip_flag[x0][y0][0]is signaled only when the condition ofIntraSubPartitionsSplit[x0][y0]==ISP_NO_SPLIT, which is the case wherethe ISP mode is not applied, is satisfied. Additionally, as shown inTable 7, transform_skip_flag[x0][y0][1] andtransform_skip_flag[x0][y0][2] may be signaled regardless of whether ornot the ISP mode is applied.

Therefore, the LFNST signaling for the case where the ISP mode isapplied may be summarized as follows. It may be assumed that otherconditions for signaling the LFNST index are already satisfied, e.g., acondition of Max(cbWidth, cbHeight)<=MaxTbSizeY is satisfied.

1. In case of a single tree

-   -   LFNST index may be signaled. And, if the LFNST index is not        signaled, the LFNST index may be inferred to be equal to 0.

2. In case of a dual tree for luma component

-   -   LFNST index may be signaled. And, if the LFNST index is not        signaled, the LFNST index may be inferred to be equal to 0.

3. In case of a dual tree for chroma component

-   -   When the transform_skip_flag[x0][y0][1] value is equal to 0, the        LfnstDcOnly variable value may be set to 0 according to the        method proposed in Table 6.    -   When the transform_skip_flag[x0][y0][2] value is equal to 0, the        LfnstDcOnly variable value may be set to 0 according to the        method proposed in Table 6.    -   When the LfnstDcOnly value is equal to 0, the LFNST index may be        signaled. And, if the LFNST index is not signaled, the LFNST        index may be inferred to be equal to 0.

When the ISP mode is applied, the LfnstDcOnly condition is not checked,as shown in Table 9. Therefore, as described above in Case 1. Singletree and Case 2. Dual tree for luma component, the LFNST index may besignaled without checking the LfnstDcOnly condition. And, in case of thedual tree for chroma, the LFNST index may be signaled according to thesame conditions specified in the case where the ISP mode is not applied,as described above in Case 3. (That is, the LFNST index may be signaledaccording to the LfnstDcOnly condition(s).)

Since transform_skip_flag[x0][y0][cIdx] values are assigned to each ofthe luma component and the two chroma components, respectively, even inthe cases of the embodiments according to Table 9, even in a case wherethe LFNST index value is greater than 0, as described in the embodimentwith reference to Table 7 (i.e., when LFNST is applied), when the LFNSTindex value is greater than 0, the LFNST may be applied only to thecomponent that is indicated by cIdx when thetransform_skip_flag[x0][y0][cIdx] value is equal to 0. The content ofthe changed specification text may be modified (or changed) to be thesame as Table 8.

If the condition of checking whether or not thetransform_skip_flag[x0][y0][0] value is equal to 0 is removed only forthe case of a dual tree, in comparison to Table 5, the LFNST indexsignaling may be configured as shown below in Table 10. The LfnstDcOnlyvariable that is shown in Table 10 may be set to 0 in accordance withthe conditions, as shown in Table 6.

TABLE 10 Descriptor coding_unit( x0, y0, cbWidth, cbHeight, cqtDepth,treeType, modeType ) {   ......   LfnstDcOnly = 1  LfnstZeroOutSigCoeffFlag = 1   MtsZeroOutSigCoeffFlag = 1  transform_tree( x0, y0, cbWidth, cbHeight, treeType, chType )  lfnstWidth = ( treeType = = DUAL_TREE_CHROMA ) ? cbWidth / SubWidthC      : ( ( IntraSubPartitionsSplitType = = ISP_VER_SPLIT ) ? cbWidth /       NumIntraSubPartitions : cbWidth )   lfnstHeight = ( treeType = =DUAL_TREE_CHROMA ) ? cbHeight / SubHeightC       : ( (IntraSubPartitionsSplitType = = ISP_HOR_SPLIT) ? cbHeight /       NumIntraSubPartitions : cbHeight )   if( Min( lfnstWidth,lfnstHeight ) >= 4 && sps_lfnst_enabled_flag = = 1 &&    CuPredMode[chType ][ x0 ][ y0 ] = = MODE_INTRA &&    ( treeType != SINGLE_TREE | |transform_skip_flag[ x0 ][ y0 ][ 0 ] = = 0 ) &&    ( treeType = =DUAL_TREE_CHROMA | | !intra_mip_flag[ x0 ][ y0 ] | |      Min(lfnstWidth, lfnstHeight ) >= 16 ) &&    Max( cbWidth, cbHeight) <=MaxTbSizeY) {    if( ( IntraSubPartitionsSplitType != ISP_NO_SPLIT | |LfnstDcOnly = = 0 ) &&     LfnstZeroOutSigCoeffFlag = = 1 )    lfnst_idx ae(v)   }   if( treeType != DUAL_TREE_CHROMA && lfnst_idx= = 0 &&    transform_skip_flag[ x0 ][ y0 ][ 0 ] = = 0 && Max( cbWidth,cbHeight ) <= 32 &&    IntraSubPartitionsSplit[ x0 ][ y0 ] = =ISP_NO_SPLIT && cu_sbt_flag = = 0 &&    MtsZeroOutSigCoeffFlag = = 1 &&tu_cbf_luma[ x0 ][ y0 ] ) {    if( ( ( CuPredMode[ chType ][ x0 ][ y0 ]= = MODE_INTER &&     sps_explicit_mts_inter_enabled_flag ) | |     (CuPredMode[ chType ][ x0 ][ y0 ] = = MODE_INTRA &&    sps_explicit_mts_intra_enabled_flag ) ) )     mts_idx ae(v)   }  }

When configuring the LFNST index signaling as shown in Table 10, in caseof the single tree, the LFNST index signaling method that is proposed inTable 7 may be applied, and, in the case of the dual tree, the methodproposed in this section (i.e., the method proposed in Table 9) may beapplied.

Similarly, since transform_skip_flag[x0][y0][cIdx] values are assignedto each of the luma component and the two chroma components,respectively, even in a case where the LFNST index value is greater than0, as described in the embodiment with reference to Table 7 (i.e., whenLFNST is applied), the LFNST may be applied to the component that isindicated by cIdx when the transform_skip_flag[x0][y0][cIdx] value isequal to 0. The content of the changed specification text has alreadybeen proposed in Table 8.

Meanwhile, an explicit description of the signaling conditions forsignaling the LFNST index according to whether or not a transform isskipped for each color component may be proposed herein according to anexample.

As shown in Table 11, the coding unit parsing table can be configured toexplicitly refer to the transform_skip_flag[x0][y0][cIdx] value in theLFNST index signaling condition (cIdx=0, 1, 2).

TABLE 11 coding_unit( x0, y0, cbWidth, cbHeight, cqtDepth, treeType,modeType ) { ......   LfnstDcOnly = 1    LfnstZeroOutSigCoeffFlag = 1   MtsZeroOutSigCoeffFlag = 1    transform_tree( x0, y0, cbWidth,cbHeight, treeType, chType )    lfnstWidth = ( treeType = =DUAL_TREE_CHROMA ) ? cbWidth / SubWidthC          : ( (IntraSubPartitionsSplitType = =  ISP_VER_SPLIT ) ? cbWidth /          NumIntraSubPartitions : cbWidth )    lfnstHeight = ( treeType= =  DUAL_TREE_CHROMA ) ? cbHeight / SubHeightC          : ( (IntraSubPartitionsSplitType = =  ISP_HOR_SPLIT) ? cbHeight /          NumIntraSubPartitions : cbHeight )   LfnstTransformNotSkipFlag = ( treeType == SINGLE_TREE ) ?         (transform_skip_flag[ x0 ][ y0 ][ 0 ] = = 0 | |     transform_skip_flag[x0 ][ y0 ][ 1 ] = = 0     | | transform_skip_flag[ x0 ][ y0 ][ 2 ] = = 0) :         ( ( treeType != DUAL_TREE_CHROMA ) ?    transform_skip_flag[ x0 ][ y0 ][ 0 ] = = 0 :    transform_skip_flag[ x0 ][ y0 ][ 1 ] = = 0 | |       transform_skip_flag[ x0 ][ y0 ][ 2 ] = = 0 ) )    if( Min(lfnstWidth, lfnstHeight ) >= 4 && sps_lfnst_enabled_flag = = 1  &&   CuPredMode[ chType ][ x0 ][ y0 ] = = MODE_INTRA &&   LfnstTransformNotSkipFlag &&    ( treeType != DUAL_TREE_CHROMA | | (!intra_mip_flag[ x0 ][ y0 ] | |       Min( lfnstWidth, lfnstHeight ) >=16 ) ) &&    Max( cbWidth, cbHeight) <= MaxTbSizeY) {    if( (IntraSubPartitionsSplitType != ISP_NO_SPLIT | | LfnstDcOnly = =  0 ) &&     LfnstZeroOutSigCoeffFlag = = 1 )      lfnst_idx ae(v)    }

In light of the operations, Table 11 is the same as Table 9. Similarly,Table 11 may also be the same as Table 10 in light of the operationswhile being configured to be the same as Table 12 so that thetransform_skip_flag[x0][y0][cIdx] value can be explicitly referred tounder the LFNST index signaling conditions of the coding unit syntaxparsing table (wherein cIdx=0, 1, 2).

TABLE 12 coding_unit( x0, y0, cbWidth, cbHeight, cqtDepth, treeType,modeType ) { ......   LfnstDcOnly = 1    LfnstZeroOutSigCoeffFlag = 1   MtsZeroOutSigCoeffFlag = 1    transform_tree( x0, y0, cbWidth,cbHeight, treeType, chType )    lfnstWidth = ( treeType = =DUAL_TREE_CHROMA ) ? cbWidth / SubWidthC          : ( (IntraSubPartitionsSplitType = =  ISP_VER_SPLIT ) ? cbWidth /          NumIntraSubPartitions : cbWidth )    lfnstHeight = ( treeType= = DUAL_TREE_CHROMA ) ? cbHeight / SubHeightC          : ( (IntraSubPartitionsSplitType = =  ISP_HOR_SPLIT) ? cbHeight /          NumIntraSubPartitions : cbHeight )   LfnstTransformNotSkipFlag = ( treeType == SINGLE_TREE ) ?        transform_skip_flag[ x0 ][ y0 ][ 0 ] = = 0 :         ( (treeType != DUAL_TREE_CHROMA ) ?     transform_skip_flag[ x0 ][ y0 ][ 0] = = 0 :     ( transform_skip_flag[ x0 ][ y0 ][ 1 ] = = 0 | |       transform_skip_flag[ x0 ][ y0 ][ 2 ] = = 0 ) )    if( Min(lfnstWidth, lfnstHeight ) >= 4 && sps_lfnst_enabled_flag = = 1  &&   CuPredMode[ chType ][ x0 ][ y0 ] = = MODE_INTRA &&   LfnstTransformNotSkipFlag &&    ( treeType = = DUAL_TREE_CHROMA | | (!intra_mip_flag[ x0 ][ y0 ] | |       Min( lfnstWidth, lfnstHeight ) >=16 ) ) &&    Max( cbWidth, cbHeight) <= MaxTbSizeY) {    if( (IntraSubPartitionsSplitType != ISP_NO_SPLIT | | LfnstDcOnly = =  0 ) &&     LfnstZeroOutSigCoeffFlag = = 1 )      lfnst_idx ae(v)    }

The following drawings are provided to describe specific examples of thepresent disclosure. Since the specific designations of devices or thedesignations of specific signals/messages/fields illustrated in thedrawings are provided for illustration, technical features of thepresent disclosure are not limited to specific terms used in thefollowing drawings.

FIG. 15 is a flowchart illustrating an operation of a video decodingapparatus according to an embodiment of the present disclosure.

Each of the steps that are disclosed in FIG. 15 is based on part of thecontents described above in FIG. 4 to FIG. 14 . Accordingly, detaileddescriptions overlapping with those described above in FIG. 3 to FIG. 14will be omitted or simplified.

The decoding apparatus 300 according to an embodiment may receiveinformation on an intra prediction mode, residual information includinga transform skip flag per individual component of a current block, andan LFNST index, and so on, from a bitstream (S1510).

More specifically, the decoding apparatus 300 may decode information onquantized transform coefficients for the target block from the bitstreamand may derive the quantized transform coefficients for the currentblock based on the information on the quantized transform coefficientsfor the current block. The information on the quantized transformcoefficients for the target block may be included in a sequenceparameter set (SPS) or a slice header and may include at least one ofinformation on whether or not a reduced transform (RST) is applied,information on the simplification factor, information on a minimumtransform size in which the reduced transform is applied, information ona maximum transform size in which the reduced transform is applied, areduced inverse transform size, and information on a transform indexindicating any one of transform kernel matrices included in a transformset.

In addition, the decoding apparatus may further receive information onan intra prediction mode for the current block and information onwhether or not the ISP is applied to the current block. The decodingapparatus may derive whether or not the current block is divided into apredetermined number of sub-partition transform blocks by receiving andparsing flag information that indicates whether to apply ISP coding orISP mode. Herein, the current block may be a coding block. Also, thedecoding apparatus may derive the size and number of dividedsub-partition blocks through flag information indicating in whichdirection the current block is to be divided.

Additionally, the decoding apparatus may receive transform skip flaginformation on individual component, i.e., luma component, Cb chromacomponent, and Cr chroma component, for the current block. Suchtransform skip flag may be received according to the tree type of thecurrent block. For example, if the tree type of the current block is asingle tree, a luma transform skip flag for the luma component, a firstchroma transform skip flag for the Cb chroma component, and a secondchroma transform skip flag for the Cr chroma component may be received.If the tree type of the current block is a dual tree luma, the lumatransform skip flag may be received. And, if the tree type of thecurrent block is a dual tree chroma, the first chroma transform skipflag and the second chroma transform skip flag may be received.

The decoding apparatus 300 may derive transform coefficients byperforming inverse quantization on residual information on the currentblock, i.e., quantized transform coefficients (S1520).

The derived transform coefficients may be arranged in a reversedirection diagonal scanning order in units of 4×4 blocks, and transformcoefficients within the 4×4 block may be arranged in reverse directiondiagonal scan order. That is, transform coefficients in which inversequantization has been performed may be disposed in a reverse scanningorder applied in a video codec, as in VVC or HEVC.

The decoding apparatus may derive modified transform coefficients byapplying the LFNST to the transform coefficients.

Unlike the first transform that separates and transforms the transformtarget coefficients along a vertical or horizontal direction, the LFNSTis a non-separated transform that applies the transform withoutseparating the coefficients along a specific direction. Suchnon-separated transform may be a low-frequency non-separated transformthat applies the forward transform only to a low-frequency regioninstead of applying the forward transform to the entire block region.

The LFNST index information may be received as syntax information, andthe syntax information may be received as a binarized bin stringincluding 0's and 1's.

The syntax element of the LFNST index according to the presentembodiment may indicate whether an inverse LFNST is applied or whetheran inverse non-separated transform is applied and may indicate any oneof the transform kernel matrices included in the transform set. And,when the transform set includes two transform kernel matrices, there maybe three values of the syntax element of the transform index.

That is, according to an embodiment, the syntax element value for theLFNST index may include 0 indicating a case where the inverse LFNST isnot applied to the target block, 1 indicating a first transformationkernel matrix among the transformation kernel matrices, and 2 indicatinga second transform kernel matrix among the transform kernel matrices.

The intra prediction mode information and LFNST index information may besignaled at a coding unit level, and the above-described transform skipflag may be signaled at a transform unit level.

In order to determine whether or not to perform parsing on an LFNSTindex for a current block, when any one transform skip value for anindividual component is equal to 0, the decoding apparatus may set avariable indicating whether or not a significant coefficient is presentin a DC component of the current block to 0 (S1530).

The variable being equal to 0 may indicate that a significantcoefficient is present at a non-DC component position of the currentblock, and such variable may be initially set to 1. That is, when avariable value, which was initially set to 1, is changed to 0, the LFNSTindex may be parsed.

A variable indicating whether a significant coefficient is present inthe DC component of the current block may be expressed as a variableLfnstDcOnly. And, for at least one transform block in one coding unit,when the non-zero coefficients are present in a non-DC component, thevalue is equal to 0, and, when the non-zero coefficients are not presentin positions other than DC components for all transform blocks in onecoding unit, the value is equal to 1. In the present disclosure, the DCcomponent indicates (0, 0) or a top-left position based on a positionreference for a 2D component.

A plurality of transform blocks may be present within one coding unit.For example, in case of the chroma component, transform blocks for Cband Cr may be present, and, in case of the single tree type, transformblocks for luma, Cb, and Cr may be present. According to an example,apart from the DC component position, if a non-zero coefficient isdiscovered (or found) even in one transform block among transform blocksconfiguring the current coding block, the value of variable LfnstDcOnlymay be set to 0.

Meanwhile, if non-zero coefficients are not present in the transformblock, since the residual coding is not performed on the correspondingtransform block, the variable LfnstDcOnly value is not changed by thecorresponding transform block. Therefore, if a non-zero coefficient isnot present in the non-DC component position of the transform block, thevariable LfnstDcOnly value is not changed, and the previous value ismaintained. For example, if the coding unit is coded as a single treetype, and if the variable LfnstDcOnly value is changed to 0 by to theluma transform block, the variable LfnstDcOnly value is maintained as 0,regardless of whether or not a non-zero coefficient is present only inthe DC component within a Cb transform block or whether or not anon-zero coefficient is present in the Cb transform block, the variableLfnstDcOnly value is maintained as 0. The variable LfnstDcOnly value isinitially initialized to 1, and, if no component in the current codingunit is capable of updating the variable LfnstDcOnly value to 0, thevariable LfnstDcOnly value is maintained as 1. And, even if one of thetransform blocks configuring the corresponding coding unit updates thevariable LfnstDcOnly value to 0, the variable LfnstDcOnly value isfinally maintained as 0.

Meanwhile, such variable LfnstDcOnly may be derived based on individualtransform skip flag values for color components of the current block.The transform skip flag for the current block may be signaled for eachcolor component, and, if the tree type of the current block is a singletree, the variable LfnstDcOnly may be derived based on the transformskip flag value for the luma component, the transform skip flag valuefor the chroma Cb component, and the transform skip flag value for thechroma Cr component. Alternatively, if the tree type of the currentblock is the dual tree luma, the variable LfnstDcOnly may be derivedbased on the transform skip flag value for the luma component, and, ifthe tree type of the current block is the dual tree chroma, the variableLfnstDcOnly may be derived based on the transform skip flag value forthe chroma Cb component and the transform skip flag value for the chromaCr component.

According to an example, based on the transform skip flag value for thecolor component being equal to 0, the variable LfnstDcOnly may indicatethat a significant coefficient is present at a position other than theDC component (or a non-DC component position). That is, if the tree typeof the current block is a single tree, the variable LfnstDcOnly may bederived as 0 based on at least one of the transform skip flag value forthe luma component, the transform skip flag value for the chroma Cbcomponent, and the transform skip flag value for the chroma Cr componentbeing equal to 0. Alternatively, if the tree type of the current blockis the dual tree luma, the variable LfnstDcOnly is derived based on thetransform skip flag value for the luma component, and, if the tree typeof the current block is the dual tree chroma, the variable LfnstDcOnlymay be derived as 0 based on the transform skip flag value for thechroma Cb component and the transform skip flag value for the chroma Crcomponent being equal to 0.

As described above, the variable LfnstDcOnly may be initially set to 1at the coding unit level of the current block, and, if the transformskip flag value is equal to 0, the variable LfnstDcOnly may be changedto 0 at the residual coding level.

Meanwhile, as described above, in case of a luma block to which theintra sub-partition (ISP) mode is applicable, the decoding apparatus mayparse the LFNST index without deriving the variable LfnstDcOnly.

More specifically, when the ISP mode is applied and the transform skipflag for the luma component, i.e., the transform_skip_flag[x0][y0][0]value is equal to 0, if the tree type of the current block is a singletree or a dual tree for luma, the LFNST index may be signaled regardlessof the variable LfnstDcOnly value.

Conversely, in case of a chroma component to which the ISP mode is notapplied, the variable LfnstDcOnly value may be set to 0 according to thetransform_skip_flag[x0][y0][1], which is the transform skip flag for thechroma Cb component, and the transform_skip_flag[x0][y0][2]. which isthe transform skip flag for the chroma Cr component. That is, in thetransform_skip_flag[x0][y0][cIdx], when the cIdx value is equal to 1,the variable LfnstDcOnly value may be set to 0 only whentransform_skip_flag[x0][y0][1] value is 0, and, when the cIdx value isequal to 2, the transform_skip_flag[x0][y0][2] value may be set to 0only when the transform_skip_flag[x0][y0][2] value is equal to 0. If thevariable LfnstDcOnly value is equal to 0, the decoding apparatus mayparse the LFNST index, and, otherwise, the LFNST index may not besignaled and may be inferred to be equal to 0.

Thereafter, based on the variable being equal to 0, the decodingapparatus may parse the LFNST index and derive an LFNST kernel forapplying the parsed LFNST index and the LFNST (S1540).

The decoding apparatus may derive modified transform coefficients thatare modified from the transform coefficients based on the LFNST kernel(S1550).

The decoding apparatus may configure a plurality of variables for theLFNST based on whether or not the LFNST index is not equal to 0, i.e.,whether or not the LFNST index is greater than 0, and whether or noteach individual transform skip flag value for a color component is equalto 0.

For example, in the step of applying the LFNST after parsing the LFNSTindex, the decoding apparatus may determine once again whether or notthe individual transform skip flag value for the color component isequal to 0, and may configure various variables for applying the LFNST.For example, the intra prediction mode for selecting the LFNST set, anumber of transform coefficients that are outputted after applying theLFNST, a size of a block to which the LFNST is applied, and so on, maybe configured.

In case of a block coded with BDPCM, the transform skip flag may beautomatically set to 1, and, in this case, even when the LFNST index isnot equal to 0, since the transform skip flag may be equal to 1, whenthe LFNST is actually applied, the transform skip flag values for eachcolor component may be checked once again.

Alternatively, according to an example, when a flag value indicatingwhether or not a coded significant coefficient is present in thetransform block is equal to 0, there may be a situation where thetransform skip flag value is not checked. In this case, also, since itis not ensured that the transform skip flag value is equal to 0 simplybecause the LFNST index is not equal to 0, when the LFNST is actuallyapplied, the transform skip flag values for each color component may bechecked once again.

That is, the decoding apparatus may check the transform skip flag valuesfor each color component in the LFNST index parsing step and may, then,check the transform skip flag values for each color component once againwhen the LFNST is actually applied.

The decoding apparatus may determine the LFNST set including the LFNSTmatrix based on the intra prediction mode that is derived from the intraprediction mode information and, then, select any one of a plurality ofLFNST matrices based on the LFNST set and the LFNST index.

At this point, the same LFNST set and the same LFNST index may beapplied to the sub-partition transform block that is divided (orpartitioned) in the current block. That is, since the same intraprediction mode is applied to the sub-partition transform blocks, theLFNST set that is determined based on the intra prediction mode may alsobe equally applied to all sub-partition transform blocks. In addition,since the LFNST index is signaled at the coding unit level, the sameLFNST matrix may be applied to the sub-partition transform block that isdivided (or partitioned) in the current block.

Meanwhile, as described above, the transform set may be determinedaccording to the intra prediction mode of the transform block that is atransform target, and inverse LFNST may be performed based on thetransform kernel matrix included in the transform set, which isindicated by the LFNST index, i.e., any of the LFNST matrices. A matrixthat is applied to the inverse LFNST may be referred to as an inverseLFNST matrix or an LFNST matrix, and the term of such matrix isirrelevant as long as it has a transpose relation with the matrix thatis used for the forward LFNST.

In an example, the inverse LFNST matrix may be a non-square matrix inwhich the number of columns is less than the number of rows.

The decoding apparatus may derive the residual samples for the currentblock based on the inverse primary transform of the modified transformcoefficient (S1560).

In this case, as the inverse primary transform, the conventionalseparation transform may be used, and the above-described MTS may beused.

Subsequently, the decoding apparatus 300 may generate reconstructedsamples based on residual samples for the current block and predictionsamples for the current block.

The following drawings were created to explain a specific example of thepresent specification. Since the names of specific devices described inthe drawings or the names of specific signals/messages/fields arepresented by way of example, the technical features of the presentspecification are not limited to the specific names used in thefollowing drawings.

FIG. 16 is a flowchart illustrating an operation of a video encodingapparatus according to an embodiment of the present disclosure.

Each step disclosed in FIG. 16 is based on some of the contentsdescribed above in FIGS. 4 to 14 . Accordingly, detailed descriptionsoverlapping with those described above in FIGS. 2 and 4 to 14 will beomitted or simplified.

The encoding apparatus 200 according to an embodiment may derive theprediction sample for the current block based on the intra predictionmode applied to the current block.

The encoding apparatus may perform prediction for each sub-partitiontransformation block when ISP is applied to the current block.

The encoding apparatus can determine whether to apply the ISP coding orthe ISP mode to the current block, that is, the coding block, anddetermine in which direction the current block is to be dividedaccording to the determination result, and derive the size and number ofdivided sub-blocks.

The same intra prediction mode may be applied to the sub-partitiontransform block divided from the current block, and the encodingapparatus may derive a prediction sample for each sub-partitiontransform block. That is, the encoding apparatus sequentially performsintra prediction, for example, horizontally or vertically, from left toright, or from top to bottom according to a division form of thesub-partition transform blocks. For the leftmost or uppermost subblock,a reconstructed pixel of an already coded coding block is referred to,as in a conventional intra prediction method. Further, for each side ofthe subsequent internal sub-partition transform block, when it is notadjacent to the previous sub-partition transform block, in order toderive reference pixels adjacent to the corresponding side, areconstructed pixel of an already coded adjacent coding block isreferred to, as in a conventional intra prediction method.

The encoding apparatus 200 may derive residual samples of the currentblock based on prediction samples (S1610).

The encoding apparatus 200 may derive a transform coefficient for thecurrent block by applying at least one of LFNST and MTS to the residualsamples, and may arrange the transform coefficients according to apredetermined scanning order.

The encoding apparatus may derive the transform coefficient for thecurrent block based on the primary transform for the residual sample(S1620).

The primary transform may be performed through a plurality of transformkernels like MTS, and in this case, the transform kernel may be selectedbased on the intra prediction mode.

The encoding apparatus 200 may determine whether to perform a quadratictransform or a non-separate transform, specifically LFNST, on thetransform coefficients for the current block, and apply the LFNST to thetransform coefficients to derive the modified transform coefficients.

The LFNST is a non-separated transform that applies the transformwithout separating the coefficients in a specific direction, unlike thefirst transform that separates and transforms the transform targetcoefficients in a vertical or horizontal direction. The non-separatedtransform may be a low-frequency non-separated transform that appliesthe transform only to a low-frequency region rather than the entiretarget block to be transformed.

The encoding apparatus checks a transform skip flag value for eachindividual component of the current block (S1630), and, when any one ofthe transform skip flag values for the individual components, i.e.,color component, is equal to 0, the encoding apparatus may set a valueof a variable, which indicates whether or not a significant coefficientis present in a DC component of the current block, to 0 (S1640).

The encoding apparatus may derive a variable indicating whether or not asignificant coefficient is present in the DC component of the currentblock by applying a plurality of LFNST matrices to the transformcoefficients, and, according to an example, may derive the modifiedtransform coefficients based on a variable indicating whether or not theISP is applied to the current block or whether or not the significantcoefficient is present in the DC component of the current blockaccording to the tree type of the current block, and the variable may bederived based on the individual transform skip flag values for the colorcomponents of the current block.

Based on the current block being a single tree type or a dual tree lumaand the ISP being applied, the encoding apparatus may apply the LFNST tothe current block, and, if the tree type of the current block is thedual tree chroma, or if the ISP is not applied, the LFNST matrix may beselected based on the variable indicating whether or not the significantcoefficient is present in the DC component.

The encoding apparatus may derive variables in a state after applyingthe LFNST to each LFNST matrix candidate, or in a state where the LFNSTis not applied when the LFNST is not applied.

More specifically, the encoding apparatus may apply a plurality of LFNSTcandidates, i.e., the LFNST matrices so as to exclude the correspondingLFNST matrix in which the significant coefficients of all transformblocks exist only in the DC position (evidently, a case where the CBF isequal to 0 is excluded from the corresponding variable determinationprocess), and to compare RD values only between the LFNST matrices inwhich the variable LfnstDcOnly value is equal to 0. For example, whenthe LFNST is not applied, the corresponding LFNST matrix is included inthe comparison process because it is irrelevant to the variableLfnstDcOnly value (in this case, since LFNST is not applied, thevariable LfnstDcOnly value may be determined based on the transformcoefficient that is obtained as a result of the primary transform), andthe LFNST matrices having the corresponding LfnstDcOnly value of 0 arealso included in the comparison process of the RD values.

variable indicating whether or not a significant coefficient is presentin the DC component of the current block may be expressed as a variableLfnstDcOnly. And, if a non-zero coefficient is present in a non-DCcomponent position for at least one transform block within a codingunit, the variable LfnstDcOnly is equal to 0, and, if a non-zerocoefficient is not present in a non-DC component position for alltransform blocks within a coding unit, the variable LfnstDcOnly is equalto 1.

A plurality of Several transform blocks may be present in one codingunit. For example, in case of the chroma component, transform blocks forCb and Cr may be present, and, in case of the single tree type,transform blocks for luma, Cb, and Cr may be present. According to anexample, when a non-zero coefficient is discovered (or found) in anon-DC component position even in one transform block, among thetransform blocks configuring the current coding block, the variableLfnstDcOnly value may be set to 0.

Meanwhile, if non-zero coefficients are not present in the transformblock, since the residual coding is not performed on the correspondingtransform block, the variable LfnstDcOnly value is not changed due tothe corresponding transform block. Therefore, if the non-zerocoefficient is not present in the non-DC component of the transformblock, the variable LfnstDcOnly value is not changed and the previousvalue is maintained. For example, when the coding unit is coded as thesingle tree type and the variable LfnstDcOnly value is changed to 0 dueto the luma transform block, the variable LfnstDcOnly value ismaintained as 0 regardless of whether or not the non-zero coefficientsare present only in the DC component in the Cb transform block, orwhether or not the non-zero coefficients are present in the Cb transformblock. The variable LfnstDcOnly value is initially initialized to 1,and, if no component in the current coding unit updates the variableLfnstDcOnly value to 0, the LfnstDcOnly value is maintained as 1 withoutbeing changed. And, if one of the transform blocks configuring thecoding unit updates the variable LfnstDcOnly value to 0, the LfnstDcOnlyvalue is finally maintained as 0.

Meanwhile, such variable LfnstDcOnly may be derived based on individualtransform skip flag values for color components of the current block.The transform skip flag for the current block may be signaled for eachcolor component, and, if the tree type of the current block is a singletree, the variable LfnstDcOnly may be derived based on the transformskip flag value for the luma component, the transform skip flag valuefor the chroma Cb component, and the transform skip flag value for thechroma Cr component. Alternatively, if the tree type of the currentblock is a dual tree luma, the variable LfnstDcOnly is derived based onthe transform skip flag value for the luma component. And, if the treetype of the current block is a dual tree chroma, the variableLfnstDcOnly may be derived based on the transform skip flag value forthe chroma Cb component and the transform skip flag value for the chromaCr component.

According to an example, based on the transform skip flag value for thecolor component being equal to 0, the variable LfnstDcOnly may indicatethat a significant coefficient is present in a non-DC componentposition. That is, if the tree type of the current block is a singletree, the variable LfnstDcOnly may be inferred to be equal to 0, basedon at least one of the transform skip flag value for the luma component,the transform skip flag value for the chroma Cb component, and thetransform skip flag value for the chroma Cr component being equal to 0.Alternatively, if the tree type of the current block is a dual treeluma, the variable LfnstDcOnly may be derived based on the transformskip flag value for the luma component being equal to 0. And, if thetree type of the current block is a dual tree chroma, the variableLfnstDcOnly may be derived based on one of the transform skip flag valuefor the chroma Cb component and the transform skip flag value for thechroma Cr component being equal to 0.

As described above, the variable LfnstDcOnly may be initially set to 1at the coding unit level of the current block, and, if the transformskip flag value is equal to 0, the variable LfnstDcOnly may be changedto 0 at the residual coding level.

The encoding apparatus derives a most optimal LFNST kernel based on thevariable being equal to 0, i.e., based on the significant coefficientbeing present in a non-DC component position (S1650), and may thenderive a modified transform coefficient based on the derived LFNSTmatrix (S1660).

The encoding apparatus may set a plurality of variables for the LFNSTbased on whether the respective transform skip flag values for the colorcomponents is 0 in the step of deriving the modified transformcoefficients.

For example, after determining whether to apply the LFNST, the encodingapparatus may determine once again whether the respective transform skipflag values for the color components are 0 in the step of applying theLFNST, and may set various variables for applying the LFNST. Forexample, the intra prediction mode for selecting the LFNST set, thenumber of transform coefficients output after applying the LFNST, thesize of a block to which the LFNST is applied, and the like may be set.

In the case of the block coded by the BDPCM, since the transform skipflag may be automatically set to 1, when the LFNST is actually applied,the transform skip flag values for each color component may be checkedagain.

Alternatively, according to an example, when the flag value indicatingwhether the coded significant coefficient exists in the transform blockis 0, there may be the situation in which the transform skip flag valueis not checked. In this case as well, since it is not guaranteed thatthe transform skip flag value is 0 just because the LFNST index is not0, when the LFNST is actually applied, the transform skip flag valuesfor each color component may be checked again.

That is, the encoding apparatus may check the transform skip flag valuesfor each color component in the step of determining whether to apply theLFNST, and may check the transform skip flag values for each colorcomponent again when the LFNST is actually applied.

Meanwhile, as described above, in the case of the luma block to whichthe intra sub-partition (ISP) mode may be applied, the LFNST may beapplied without deriving the variable LfnstDcOnly.

Specifically, when the ISP mode is applied and the transform skip flagfor the luma component, that is, the transform_skip_flag[x0][y0][0]value is 0, the tree type of the current block is a single tree or adual tree for luma, the LFNST may be applied regardless of the variableLfnstDcOnly value.

On the other hand, in the case of the chroma component to which the ISPmode is not applied, the variable LfnstDcOnly value may be set to 0according to the transform_skip_flag[x0][y0][1] which is the transformskip flag for the chroma Cb component and transform_skip_flag[x0][y0][2]which is the transform skip flag for the chroma Cr component. That is,in the transform_skip_flag[x0][y0][cIdx], when the cIdx value is 1, onlywhen transform_skip_flag[x0][y0][1] value is 0, the variable LfnstDcOnlyvalue may be set to 0, and when the cIdx value is 2, thetransform_skip_flag[x0][y0][2] value may be set to 0 only when thetransform_skip_flag[x0][y0][2] value is 0. If the variable LfnstDcOnlyvalue is 0, the encoding apparatus may apply the LFNST, otherwise theLFNST is not applied.

The encoding apparatus 200 may determine the LFNST set based on amapping relationship according to the intra prediction mode applied tothe current block, and perform an LFNST, that is, a non-separabletransform based on one of two LFNST matrices included in the LFNST set.

In this case, the same LFNST set and the same LFNST index may be appliedto the sub-partition transform block divided from the current block.That is, because the same intra prediction mode is applied to thesub-partition transform blocks, the LFNST set determined based on theintra prediction mode may also be equally applied to all sub-partitiontransform blocks. Further, because the LFNST index is encoded in unitsof a coding unit, the same LFNST matrix may be applied to thesub-partition transform block divided from the current block.

As described above, a transform set may be determined according to anintra prediction mode of a transform block to be transformed. A matrixapplied to LFNST has a transpose relationship with a matrix used for aninverse LFNST.

In one example, the LFNST matrix may be a non-square matrix in which thenumber of rows is smaller than that of columns.

The encoding apparatus may construct the image information so that theLFNST index instructing the LFNST matrix applied to the LFNST is parsedbased on the fact that the variable LfnstDcOnly is initially set to 1 inthe coding unit level of the current block, and when the transform skipflag value is 0, the variable LfnstDcOnly is changed to 0 in theresidual coding level, and the variable LfnstDcOnly is 0.

The encoding apparatus may perform quantization based on the modifiedtransform coefficients for the current block to derive quantizedtransform coefficients, and encode an LFNST index.

That is, the encoding apparatus may generate residual informationincluding information on quantized transform coefficients. The residualinformation may include the above-described transform relatedinformation/syntax element. The encoding apparatus may encodeimage/video information including residual information and output theencoded image/video information in the form of a bitstream.

More specifically, the encoding apparatus 200 may generate informationabout the quantized transform coefficients and encode the informationabout the generated quantized transform coefficients.

The syntax element of the LFNST index according to the presentembodiment may indicate whether (inverse) LFNST is applied and any oneof the LFNST matrices included in the LFNST set, and when the LFNST setincludes two transform kernel matrices, there may be three values of thesyntax element of the LFNST index.

According to an embodiment, when a division tree structure for thecurrent block is a dual tree type, an LFNST index may be encoded foreach of a luma block and a chroma block.

According to an embodiment, the syntax element value for the transformindex may be derived as 0 indicating a case in which (inverse) LFNST isnot applied to the current block, 1 indicating a first LFNST matrixamong LFNST matrices, and 2 indicating a second LFNST matrix among LFNSTmatrices.

In the present disclosure, at least one of quantization/dequantizationand/or transform/inverse transform may be omitted. Whenquantization/dequantization is omitted, a quantized transformcoefficient may be referred to as a transform coefficient. Whentransform/inverse transform is omitted, the transform coefficient may bereferred to as a coefficient or a residual coefficient, or may still bereferred to as a transform coefficient for consistency of expression.

In addition, in the present disclosure, a quantized transformcoefficient and a transform coefficient may be referred to as atransform coefficient and a scaled transform coefficient, respectively.In this case, residual information may include information on atransform coefficient(s), and the information on the transformcoefficient(s) may be signaled through a residual coding syntax.Transform coefficients may be derived based on the residual information(or information on the transform coefficient(s)), and scaled transformcoefficients may be derived through inverse transform (scaling) of thetransform coefficients. Residual samples may be derived based on theinverse transform (transform) of the scaled transform coefficients.These details may also be applied/expressed in other parts of thepresent disclosure.

In the above-described embodiments, the methods are explained on thebasis of flowcharts by means of a series of steps or blocks, but thepresent disclosure is not limited to the order of steps, and a certainstep may be performed in order or step different from that describedabove, or concurrently with another step. Further, it may be understoodby a person having ordinary skill in the art that the steps shown in aflowchart are not exclusive, and that another step may be incorporatedor one or more steps of the flowchart may be removed without affectingthe scope of the present disclosure.

The above-described methods according to the present disclosure may beimplemented as a software form, and an encoding apparatus and/ordecoding apparatus according to the disclosure may be included in adevice for image processing, such as, a TV, a computer, a smartphone, aset-top box, a display device or the like.

When embodiments in the present disclosure are embodied by software, theabove-described methods may be embodied as modules (processes, functionsor the like) to perform the above-described functions. The modules maybe stored in a memory and may be executed by a processor. The memory maybe inside or outside the processor and may be connected to the processorin various well-known manners. The processor may include anapplication-specific integrated circuit (ASIC), other chipset, logiccircuit, and/or a data processing device. The memory may include aread-only memory (ROM), a random access memory (RAM), a flash memory, amemory card, a storage medium, and/or other storage device. That is,embodiments described in the present disclosure may be embodied andperformed on a processor, a microprocessor, a controller or a chip. Forexample, function units shown in each drawing may be embodied andperformed on a computer, a processor, a microprocessor, a controller ora chip.

Further, the decoding apparatus and the encoding apparatus to which thepresent disclosure is applied, may be included in a multimediabroadcasting transceiver, a mobile communication terminal, a home cinemavideo device, a digital cinema video device, a surveillance camera, avideo chat device, a real time communication device such as videocommunication, a mobile streaming device, a storage medium, a camcorder,a video on demand (VoD) service providing device, an over the top (OTT)video device, an Internet streaming service providing device, athree-dimensional (3D) video device, a video telephony video device, anda medical video device, and may be used to process a video signal or adata signal. For example, the over the top (OTT) video device mayinclude a game console, a Blu-ray player, an Internet access TV, a Hometheater system, a smartphone, a Tablet PC, a digital video recorder(DVR) and the like.

In addition, the processing method to which the present disclosure isapplied, may be produced in the form of a program executed by acomputer, and be stored in a computer-readable recording medium.Multimedia data having a data structure according to the presentdisclosure may also be stored in a computer-readable recording medium.The computer-readable recording medium includes all kinds of storagedevices and distributed storage devices in which computer-readable dataare stored. The computer-readable recording medium may include, forexample, a Blu-ray Disc (BD), a universal serial bus (USB), a ROM, aPROM, an EPROM, an EEPROM, a RAM, a CD-ROM, a magnetic tape, a floppydisk, and an optical data storage device. Further, the computer-readablerecording medium includes media embodied in the form of a carrier wave(for example, transmission over the Internet). In addition, a bitstreamgenerated by the encoding method may be stored in a computer-readablerecording medium or transmitted through a wired or wirelesscommunication network. Additionally, the embodiments of the presentdisclosure may be embodied as a computer program product by programcodes, and the program codes may be executed on a computer by theembodiments of the present disclosure. The program codes may be storedon a computer-readable carrier.

FIG. 17 illustrates the structure of a content streaming system to whichthe present disclosure is applied.

Further, the contents streaming system to which the present disclosureis applied may largely include an encoding server, a streaming server, aweb server, a media storage, a user equipment, and a multimedia inputdevice.

The encoding server functions to compress to digital data the contentsinput from the multimedia input devices, such as the smart phone, thecamera, the camcorder and the like, to generate a bitstream, and totransmit it to the streaming server. As another example, in a case wherethe multimedia input device, such as, the smart phone, the camera, thecamcorder or the like, directly generates a bitstream, the encodingserver may be omitted. The bitstream may be generated by an encodingmethod or a bitstream generation method to which the present disclosureis applied. And the streaming server may store the bitstream temporarilyduring a process to transmit or receive the bitstream.

The streaming server transmits multimedia data to the user equipment onthe basis of a user's request through the web server, which functions asan instrument that informs a user of what service there is. When theuser requests a service which the user wants, the web server transfersthe request to the streaming server, and the streaming server transmitsmultimedia data to the user. In this regard, the contents streamingsystem may include a separate control server, and in this case, thecontrol server functions to control commands/responses betweenrespective equipments in the content streaming system.

The streaming server may receive contents from the media storage and/orthe encoding server. For example, in a case the contents are receivedfrom the encoding server, the contents may be received in real time. Inthis case, the streaming server may store the bitstream for apredetermined period of time to provide the streaming service smoothly.

For example, the user equipment may include a mobile phone, a smartphone, a laptop computer, a digital broadcasting terminal, a personaldigital assistant (PDA), a portable multimedia player (PMP), anavigation, a slate PC, a tablet PC, an ultrabook, a wearable device(e.g., a watch-type terminal (smart watch), a glass-type terminal (smartglass), a head mounted display (HMD)), a digital TV, a desktop computer,a digital signage or the like. Each of servers in the contents streamingsystem may be operated as a distributed server, and in this case, datareceived by each server may be processed in distributed manner.

Claims disclosed herein can be combined in a various way. For example,technical features of method claims of the present disclosure can becombined to be implemented or performed in an apparatus, and technicalfeatures of apparatus claims can be combined to be implemented orperformed in a method. Further, technical features of method claims andapparatus claims can be combined to be implemented or performed in anapparatus, and technical features of method claims and apparatus claimscan be combined to be implemented or performed in a method.

What is claimed is:
 1. An image decoding method performed by a decodingapparatus, comprising: receiving residual information from a bitstream,wherein the residual information includes a transform skip flag for eachindividual component of a current block; deriving transform coefficientsfor the current block based on the residual information; and derivingmodified transform coefficients by applying LFNST to the transformcoefficients, wherein the deriving modified transform coefficientscomprises: setting a variable indicating whether or not a significantcoefficient is present in a non-DC component position of the currentblock to 0 when any one of values of the transform skip flag for theindividual components is equal to 0; parsing an LFNST index based on thevariable being equal to 0; and deriving an LFNST kernel for applying theLFNST based on the LFNST index, wherein the variable being equal to 0indicates that the significant coefficient is present in the non-DCcomponent position.
 2. The image decoding method of claim 1, wherein,when the current block is a single tree type, a luma transform skip flagfor a luma component, a first chroma transform skip flag for a firstchroma component, and a second chroma transform skip flag for a secondchroma component are received, and wherein, when any one of a value ofthe luma transform skip flag, a value of the first chroma transform skipflag, and a value of the second chroma transform skip flag is equal to0, the variable is set to
 0. 3. The image decoding method of claim 2,wherein, based on ISP being applied to the current block, the LFNSTindex is parsed regardless of a value of the variable.
 4. The imagedecoding method of claim 1, wherein, when the current block is a dualtree luma, a luma transform skip flag for a luma component is received,and wherein, when a value of the luma transform skip flag is equal to 0,the variable is set to
 0. 5. The image decoding method of claim 4,wherein, based on ISP being applied to the current block, the LFNSTindex is parsed regardless of a value of the variable.
 6. The imagedecoding method of claim 1, wherein, when the current block is a dualtree chroma, a first chroma transform skip flag for a first chromacomponent and a second chroma transform skip flag for a second chromacomponent are received, and wherein, when any one of a value of thefirst chroma transform skip flag and a value of the second chromatransform skip flag is equal to 0, the variable is set to
 0. 7. Theimage decoding method of claim 1, wherein the deriving modifiedtransform coefficients further comprises: setting a plurality ofvariables for the LFNST based on the LFNST index not being equal to 0and whether or not a value of the individual transform skip flag for thecolor component is equal to
 0. 8. An image encoding method performed byan image encoding apparatus, comprising: deriving prediction samples fora current block; deriving residual samples for the current block basedon the prediction samples; deriving transform coefficients for thecurrent block based on a primary transform for the residual samples; andderiving modified transform coefficients from the transform coefficientsby applying LFNST and, wherein the deriving modified transformcoefficients comprises: checking a value of a transform skip flag foreach individual component of the current block; setting a variableindicating whether or not a significant coefficient is present in anon-DC component position of the current block to 0 when any one ofvalues of the transform skip flag for each individual component is equalto 0; and deriving an LFNST kernel for applying the LFNST based on thevariable being equal to 0, wherein the variable being equal to 0indicates that the significant coefficient is present in the non-DCcomponent position.
 9. The image encoding method of claim 8, wherein,when the current block is a single tree type, a luma transform skip flagfor a luma component, a first chroma transform skip flag for a firstchroma component, and a second chroma transform skip flag for a secondchroma component are checked, and wherein, when any one of a value ofthe luma transform skip flag, a value of the first chroma transform skipflag, and a value of the second chroma transform skip flag is equal to0, the variable is set to
 0. 10. The image encoding method of claim 9,wherein, based on ISP being applied to the current block, the LFNSTindex is applied regardless of a value of the variable.
 11. The imageencoding method of claim 8, wherein, when the current block is a dualtree luma, a luma transform skip flag for a luma component is checked,and wherein, when a value of the luma transform skip flag is equal to 0,the variable is set to
 0. 12. The image encoding method of claim 11,wherein, based on ISP being applied to the current block, the LFNSTindex is applied regardless of a value of the variable.
 13. The imageencoding method of claim 8, wherein, when the current block is a dualtree chroma, a first chroma transform skip flag for a first chromacomponent and a second chroma transform skip flag for a second chromacomponent are checked, and wherein, when any one of a value of the firstchroma transform skip flag and a value of the second chroma transformskip flag is equal to 0, the variable is set to
 0. 14. A computerreadable digital recording medium having information stored therein thatcauses a video decoding method to be performed, wherein the videodecoding method comprises: receiving residual information from abitstream; deriving transform coefficients for a current block based onthe residual information; deriving modified transform coefficients byapplying LFNST to the transform coefficients; wherein the derivingmodified transform coefficients comprises: receiving a transform skipflag value for each individual component of the current block; setting avariable indicating whether or not a significant coefficient is presentin a non-DC component position of the current block to 0 when any one ofvalues of the transform skip flag for the individual components is equalto 0; parsing an LFNST index based on the variable being equal to 0; andderiving an LFNST kernel for applying the LFNST based on the LFNSTindex, wherein the variable being equal to 0 indicates that thesignificant coefficient is present in the non-DC component position.